Must be a very leaky house - or a poor system. Do your rads get hot?
One of the cheapest and most effective things you can do is loft insulation.
I've steadily made improvements over the years (1980s 3 bed semi)
Better loft insulation (but not perfect because I've boarded out the central third for storage space)
Fitted some insulation to the loft hatch last year
Double glazing was done about 15yrs ago
Blocked up the air bricks.
Just had new front/back doors to replace the original poorly sealed single glazed doors.
I've had the heating on all day recently (off overnight). Thermostat set to 19.5C. My smart meter tells me last week cost me £23.60 - the highest of the winter so far. In the cold weather last week the house cooled to a little under 16C overnight
To replace the GCH with ASHP I'd need to replace the pipework to the rads with larger diameter because I have microbore pipes at the minute which won't work well for a high flow system