Grantham. 1h10m to Kings Cross. There are a handful of 5-bed detached houses within budget.
A season ticket to Kings Cross will set you back £845 a month; or £914 if you need the tube too. That would go a long way towards a mortgage closer to London.
How detached do you want? Some houses are notionally detached but barely an alleyway’s width away from the neighbours, and with small gardens to boot.