It's impossible to tell what variety it is without seeing the fruit but one thing is clear - it doesn't look too good. Don't over-water it and give it plenty of ventilation (not draughts) and stake it. If that tomato plant bears heavy trusses it will definitely need staking - but you knew that anyway. And something else, you are supposed to remove all side growths (the bit that grows from each leaf axil) if you don't the plant will go on producing growth instead of fruit and when the fifth (optional) truss has set stop the plant (remove the growing tip)

I doubt anyone can really tell you which variety you have. so I would treat them as needing support at least then you are covering all the bases.

About a month ago we bought some tomato plants as baby's, I know that some varietys need supports from bamboo sticks but not all do, I lost the thing telling me what they were called and it would be useful if someone could identify them and tell me wether they are the types that need bamboo supports or not?

Thanks in advance.

Ps. It has a few small yellow leaves shown badly in pic.