KLM certainly offer very quick connections at Amsterdam, down to 40 minutes I believe. I'm sure they wouldn't do it if it wasn't at least possible, but it is indeed tight. Whilst many travellers can be assured that they will be offered conveyance to their final destination, missing a tight connection regularly on your commute would be very problematic (and a weekly phone call to your boss saying you're stuck in Amsterdam probably won't go down too well!).
For non-Schengen to non-Schengen connections, you do not currently need to pass through security again. So UK-UK via Amsterdam would not require a security check in Amsterdam. But if your hand luggage was checked at the gate due to the flight being busy (this is quite common with both KLM and easyJet) you could be stuck having to pass through immigration and clear security again (basically you'll miss your flight if it's a tight connection). Amsterdam is a very big airport, and there's a good walk between each concourse. D-H would take quite some time. If it is KLM-easyJet, it's a long walk/run.
What the OP is asking is very tough. easyJet and flyBe usually use the H gates from what I remember, KLM and BA tend to use D (although I have seen flyBe go from the D gates on occasion, possibly using the remote stands), so you're looking at a very tight connection in Amsterdam, and 45 minutes allows precisely no contingency time. I think you will run into problems more often than not, and would suggest that you try an alternative route.