How much will it cost?

[Housebuying2]

Replacing electric storage heating with a new gas boiler and radiators.

3 bedrooms, 2 bathrooms, 3 reception rooms & kitchen, hall and landing.

ballpark figure?

A lot! Where in UK are you.

A least £1900 just for the boiler
I’d say similar fior rads, pipework (under floorboards 🥴) and labour but obviously depends where you live

Around £6-8k inc labour

It's open heart surgery on your house. Its the pipework that will take the time (and a chunk of labour costs) - do you want the pipes hidden downstairs? You'll have floors to come up, or pipework to be buried in walls. Chased and filled etc.
Boiler, dozen rads, thermostat, condensate routing and all that new pipework. Possibly closer to £10k.

my parents had similar installed back in 2017

cost around 4500 for the boiler and radiators and then around 1k to connect the gas to the meter from the street
This was a large 2 bed Victorian Terrace
radiators in the following rooms
2 living rooms
2 bedrooms
kitchen
bathroom
utility room
hallways downstairs / upstairs

i think they had around 10 radiators in total and heated bathroom towel rail

but they didn’t have the pipe work chased inn/ hidden
they did that at a later time

they never had any type of heating at all

avoid British Gas as they quoted 8k not including connection

South coast

No gas in the house but it's at the pavement. No piping etc. literally just a few electric storage heaters and an immersion tank.