Cost of engine rebuild...what should I do?

Give these chaps a ring, they can call out and analyse.
https://www.roughluckracing.com/servicing/

Rough luck gets a double thumbs up from me. However there are a considerable number of double thumbuppers out there to keep him going for a while, Jon will have a list in his little black book. Jump on soon rather than later.
If it were to be a valve stem oil seal, he & Claire would come prepared with a freshly refurbished unit to match your engine & when they leave in the evening your car will have everything miscreant item replaced & your MOT would be a forgone conclusion. Providing the catalyst is good & it’s been cooked at gas mark 70 after a hard run.
Bitz would sort you a good replacement though.
M

After a consultation with the garage I asked would the car be worth the investment of engine work...his response that is honest is due to the unknowns when entering the dissasembley , will it all come apart easily enough for starters due to possible broken or seized parts , and the second lot of welding that he has just completed he recommends I put my money in to another one.
Therefore I will be trying to sell it as is or break it up as it has many good parts on it that I will mention eventually when I get sorted. Disappointing as it is he reckons that the rot underneath may make the engine investment not worth while in 12-18 months.

Some attached pics of her🙁

There is some great advice here, you have obviously spent a lot of time and money and it would be a shame to break it.

There are many reasons why it could fail the emissions test but if you're not getting smoke from the exhaust then I wouldn't think that the engine was your problem. 

A bad sensor or cat could be your problem. 

I think it escapes those whose formal attire is a boiler suit & a manicure happens when your hand gets trapped under a poorly supported chunk of Abingdons finest. The cost of professional services, particularly on an ageing car could easily outweigh the vehicles value.
I acquired my tf due to the original owner not wishing to spend any more money on it. After minimal work it proved to be a great car.
The continuing depression in tf prices can lead to the vehicles dissolution (a gentlemanly euphemism for scrap) & just looking at the pictures might create interest in the wheels, four pots & discs. It wouldn’t take long for those items, If in good condition, to be more valuable as parts than if they were attached to a car for sale
I know that this is contentious, so don’t mutter your displeasure at my comments to yourself, become that “keyboard warrior” you always knew yourself to be & bollock me for my heretical thoughts, if you do wish.
M

I wouldn't be too hasty in blaming the engine itself either, it could be a failure for any number of reasons other than the engine itself, it needs a good diagnostic going over with a check to see if the Pscan throws up a fault, further checks on compression  exhaust manifold pressure etc, are essential before condemning the engine or car for that matter.
Most problems seem huge until you actually find what it is that has gone wrong, the trick is zeroing in on the source of your woes, now it's easy for me to say all this from the other side of the world, but it's a pity that I can't see the car for myself.

But blaming the head gasket with out any evidence, that it is the cause is a bit like blaming a broken leg on a heart attack, out of context , it makes no sense
 the heart attack may have set in train a series of events that resulted in the broken leg, but without any evidence to prove it.....there is bugger all to link the two!

Which reminds me of something that happened here in Oz back in the 60's at the Bathurst endurance race, one of the cars had an obvious case of the engine doing an impression of a had grenade going off, with a huge cloud of oil smoke, oil all over the place and a nice mix of engine internal allsorts deposited upon the track.
The TV commentator interviewing the driver asked what had gone wrong? the driver replied dryly that the alternator fell off! The bloke from the telley was incredulous and asked how that could cause the the spectacle witnessed, the driver replied that the conrod let go, punching it's way out of the engine block, knocking the alternator off!

Here is a view without knowing the details.

I have a good relationship with a very reliable nearby garage who is happy to do work on our cars or just an MOT with the same customer satsifaction.
They even encourage me to do my own work on our cars.
My TF failed on emissions and it has an after-market "short" CAT.
My mistake was to present the car relatively cold. The water was up to normal but the engine itself was not.
The garage principal told me that many modles of car suffer from the same problem. They are fine when fully warm.

Could this cause help you pass?.......

I would try the actions mentioned earlier, and maybe a cylinder compression check. See if there's a lot of coming from the crankcase breather (Sign of piston ring blow by) Are the plugs getting oily? Is the engine using oil?

Could you post the results of the emissions test? Someone on here maybe able to point you in the right direction. 

I appreciate everybody's input...all tests were done to try and bring the emissions back in but they were well out not just too high!!
I've had genuine cats fitted only a couple of years ago with every possible conceivable item thrown at it..lambda sensors repeatedly.. all cleaners to try and clear up the emissions. The head gasket isn't the issue here it's the fact that the head needs to come off to diagnose anything untoward and replaced so there's best part of £700 before anything else!!
I haven't got anywhere to store it at home until another recommended party is able to look at it as I know it can take months due to their popularity.
As the garage said they are happy to do the work and I'm happy to pay for it if I thought it was a viable option but the rest of the car is going to need some sort of restoration following on from this and there comes a point when you have to weigh up your options!

Just off the top of my head there's a full leather interior, x4 decent 16"alloys with x4 toyos that haven't done more than 6-700 miles! 4 pots only a few years old. Spax adjustables with H&R springs.. 4-2-1 ,matching hardtop loads of history, just paid £450 for the failed mot, full service lanoguard top up etc..so if anyone wants to take it as is please do so but it's off the road due to the failed test so needs towing!!
This is gutting but I need it gone before I really consider my next option!

Unless there is evidence to suggest otherwise the engine itself WONT be the cause of your problems, the cause will be peripheral. The bloke who does the work on your car may well have missed something, it happens to the beat of us! Which is why I suggest a fresh set of eyes, some times you can't see the wood from the trees.

Now the rust etc is entirely another matter and I can't help you with that part of the decision from afar.

But do you intend to replace the car with another MGF/TF?  if so I'd hang on to this one and swap over any desirable/better/new bits over to it's replacement. before unloading the current car. Yes I realise space may be a problem but it is a short term problem, that requires you to find away how to swing it.

It's not how many problems or how big those problems are, but how you go about tackling them that defines you.