1. In a nutshell, is the whole DIY Sub thing the harmonious marriage of cabinet volume (in litres sq) + driver + amp?
Yup you got it! You would usually fill the cabinet with stuffing (not Sage and Onion) when building a sealed enclosure, which is easier than a vented one (i.e. it has a reflex port - this needs "tuning" in length and adds to the fiddling factor).
2. Can anyone suggest a UK online retailer and part/catalogue no. for the input/amplifier/bit with the volume & cutoff knobs on. I'm not entirely sure of the true name for that particular component
http://www.bkelec.com. Click on the "modules and hybrids" button. You want either one of the British Sub Bass (BSB) or Class D panels (DT 150/300).
http://www.cpc.co.uk also stock one for around £120. I'd recommend BK though, as they can offer a bundle with those DT amps with a suitable bass driver.
3. What does 'flat' refer to in Subwoofer terms?
It's to do with frequency response. The idea with any speaker is for the output signal's amplitude (i.e. volume) to be the same at all frequencies, otherwise a particular frequency will be exaggerated. Obviously any speaker is limited by its physical design, and will only go so low. When someone says the speaker is "flat to 20Hz" for instance, they are saying that it is capable of outputting a decent sound level right down to 20Hz, which is quite low, and capable of flapping any teenager's flares. The image attached is "flat" to 30Hz.
4. Does the output from the amp unit described in Q2 connect directly to the driver?
Yes. You have a low level (i.e. unamplified) signal from the AV amp (the output from the subwoofer connector), which runs to the sub amp's input. The sub amp amplifies it, and this then goes to the driver.
5. Once all the tech details are taken into account it all seems fairly straight forward. Is there something that I'm overlooking that would make such a project not so?
Make sure the cabinet is airtight - might be worth buying the MDF from somewhere that will cut it for you - that way you get nice sharp square edges, and all the same size (hopefully). There are plenty of recommended designs to suit particular drivers out there - don't get hung up on "getting it flat to 20Hz", as this will require a large cabinet and beefy amp and driver. There's a bloke called Tom at BKElec who's fairly helpful

and will guide you to a suitable combo - he's the guy who tends to answer the emails you send to BK.
Think about the space you have available for a sub, as well as the room size. Don't forget that the cabinet volume will be reduced by adding the amp and driver, so take that into account when working out your cabinet dimensions.
HTH!