I'm sure this question comes up a lot and you guys must be a little sick of answering it but I'm a little unsure of my options.

I was previously a regular traveller to the US and Japan and I've always travelled on Virgin (VS) previously. I'm a silver member of their FF program but due to changes in projects and role I don't seem to be flying them much anymore.

My company is very cost centric so I generally always fly economy and I have very little influence over the choice of carrier. I've flow TG, TK and LH in the past 6mo and I expect to be doing 4 or 5 more flights on LH/TK over the next couple of years. My trips are mostly based in Europe (I'm in the UK).

My understanding is that I need to pick a carrier to join and they will then get my miles. I was thinking that given I'm based in the UK I might be better off joining the BMI (BD) plan even though I'm unlikely to fly with them any time other than claiming the rewards as they seem to have easy requirements for jumping levels. Is this the case or would I be better of picking one of the airlines I actually fly. I don't even know if I can join the FFP for an airline I've not flown with. Also can I claim miles for flights taken before I joined the *A scheme - is that specific to any individual program?

Any thoughts would be appreciated.

Well, flying economy it's tricky.
It depends on the actual booking classes.
If it's cheap classes you may be best off with UA MP , even if you never fly them, as they tend do give 100% miles for most booking classes.
BMI DC, though in principle looking nice, oftentimes only gives 25-50% of flown miles for TK and LH flights.
TK M&S will at least give full credit for TK flights and also for many LH classes.
TG has booking classes that give miles nowhere.

You can join every FF program you like. And better do it for the carriers you fly at least (and maybe a few more).
Crediting flights you've already taken may work (or not), depending on program. Chances are that you can get credit for flights maybe a month or 3 back with the program of the airline flown (YMMV ).
Once you joined a program you can expect that you can credit flights dating back several months even if your number was not in the booking.

Thank you for the tips.

You answer leads me to another question. Do the programs cross reference the claimed flights? I was assuming they do.
If for example I join TK and BD FFPs can I claim a flight I make on TK with both?

No, you can only claim it once. Whatever number is on your boarding pass, thats the program you will claim with.