We would fit the rads and pipework ourselves and get the plumber to do
the boiler. Around £1500 (maybe a little bit more) to spend on boiler
inc fitting.

OK, if you're happy doing the radiators, you'd be happy fitting a heat bank.
It is plumbed in just like a radiator, but with additional mains cold in and
hot water out. It is much more suited to quick DIY installations than a
mains pressure cylinder, which has to have all sorts of additional safety
equipment, pressure relief runs etc.

So, I would narrow your choices to a high flow combi and a heat bank system.
Something like:

Worcester Bosch HE35+ for 1140 inc VAT. (instant combi)

or

DPS Pandora + Worcester Bosch HE28 for around 1500 inc VAT total.

You'll need to budget a few hundred to get a CORGI round to install the
gas/flue, if you're not happy to describe yourself as competent for these
tasks. You'll need more if it requires a new gas run.

Note that you won't get the full benefit of the heat bank at only 21lpm,
although it will still be noticeably quicker than the combi and less prone
to temperature fluctuation. However, you may find that after rejigging, the
total throughput of water in the house actually exceeds 21lpm anyway.
Kitchen taps often aren't as wide bored as they used to be and you can find
the bathroom taps, with their twin wider passages can pass more water.

If you are replumbing the house, consider replacing all cold water pipework
with 22mm bore (except runs to toilets and basins). Provided pressure is
high enough, I'd then use 15mm for hot water pipework between tank and
kitchen and either 15mm or 22mm from tank to bathroom, remembering that
there will be more wastage and longer lead times if 22mm is used, although
it might marginally increase flow rate.

Christian.