Yarwell's answer goes down the proper technical route to investigating. Answer him before coming back to this one...
If anyone could explain to me why this is like this then I would be completely happy to read a whole book worth of text about it.
The textbooks you really want are on economics, not on physics or communications theory.
Your neighbour has access to Virgin, but you don't, and that appears to be the major difference between the two right now.
Why? Virgin don't supply everyone - the regional companies that originally installed cable cherry-picked the most profitable areas, and were given government protection from competition, but still failed to make any money. After many takeovers, mergers and liquidations, Virgin has emerged as the one main national cable company. It is saddled with debt, and can't afford to expand.
And for regulatory reasons, it would appear to now WANT to get any bigger either - presumably for fear of being forced to allow other ISPs to deliver service over its cable (in much the same way as BT is forced to allow other ISPs to serve over copper and fibre).
What about BT's fibre - either FTTC or FTTP?
Well, the fact is that this rollout is governed by economics too.
1st, it can't happen for everyone overnight - that would be just too expensive. Someone has to be first, and someone has to be last. You might yet get the rollout.
2nd, it only happens where it is profitable. If BT has decided not to convert your cabinet, it is normally for economic reasons.
3rd, where un-economic, the government has decided the economics instead. They have allocated gap funding to subsidise areas as part of the BDUK process - and allocated £0 to Greater London. There is supposedly money for "connected cities", but I haven't seen plans for this to improve residential broadband in the suburbs.
4th is a technical issue - that your line can't handle fibre broadband, usually because it is too far from the converted cabinet, or because there is no cabinet at all. These aren't impossible issues to solve, but they take money... so we're back to the economics too. However, these are also the issues that BT tend to be holding back to the end of the rollout so you're back to issue 1 there.
P.S. I live in Harrow,Middlesex
Ah - there's the problem. The government think Middlesex doesn't exist any more, so didn't give it any money!
Seriously though, your best bet to finding out about superfast broadband is to contact Openreach, giving address and phone number details. Their email address is nga.enquiries at openreach.co.uk
It might also be worthwhile finding out if Virgin could be persuaded to extend coverage. Unlikely, but it has happened.