All the UK AeMCs are (I believe) dual approved to do both UK CAA and EASA class one initials. You should definitely book to do both when you go. Though the price is quite high, it's totally worth it to know that both paths are open for you. Plus it works out cheaper and much easier than doing one class one in the UK and then another an EASA member state.
In terms of what to do for training. You only need to do the training once - but need to go to somewhere with both UK and EASA approvals (post-PPL). That's why the costs aren't that might greater.
For ATPLs, it's quite easy as many providers are dual approved and one course covers both. You can sit EASA exams in lots of places in the UK too. For example, you can do the course with BGS or CATS or no doubt others and sit both UK and EASA exams at their centre. Yes, you need to sit 26 exams, but you can do UK POF one day and EASA POF the next and they are basically the same exam with the same syllabus.
For the CPL/IR, things get a little trickier. There are dual approved ATOs, but you really need to look into it. You are right above that courses in the UK tend to be pricier, but it's not really a fair comparison to look at only Poland or Hungary as UK courses are no more expensive than EASA courses in France or Germany. There are some UK CAA approved ATOs outside of the UK so the training doesn't have to be in the UK***. Again the differences between the UK and EASA regulations are basically zero so there's no real difference in training.
For the CPL, it's not so difficult. You do the course at a dual approved ATO and then do a single skills test. You need a dual UK and EASA examiner to do that, but they are not that uncommon.
***The 'gotcha' is the IR skills test. You'll have to do it twice - once in UK airspace and once in EASA airspace. I know some schools like Stapleford have you ferry the plane to France to do it there which is sensible. Other schools like FTE Jerez in Spain have a UK partner - you do the training and the EASA IR in Spain and then do some familiarization flights and then the UK skills test in the UK with their partner school.
For the MCC, again there are plenty of dual approved places like Simtech or VA or Stapleford. A-UPRT is the same - plenty of dual approved places.
Then you are ready to go with both licenses. Extra cost likely under £5k (small in the grand scheme of things), but keeping all available options open to you.