Earlier quoted context omitted.
On my street, my house is one of 4 connected directly to the exchange instead of a cabinet, which means I can't get fibre (only FTTC is available here). BT/Openreach/Whoever aren't interested in changing this, but luckily I can get Virgin Media (overpriced IMO, but better than the 20Mb alternative).
Openreach certainly are interested in converting homes from EO to a street cabinet and have done this many times, but that's little comfort to you because they haven't done yours yet. In some cases Openreach converts from EO to FTTP, so you go from only having very poor ADSL2 available to 300Mbps or better available over fibre.
Probably the faster connection has some latency benefit, but on the whole I wouldn't factor "super fast Internet" into choosing my next place to live