I think (from the descriptions) you have one of two, or two issues.
Firstly and most likely, the battery is knackered. If the dasboard lights up but the engine is slow to crank over (or clicks, or is completely unresponsive/lights dim) then you need to charge up or replace the battery (if it's too far gone/damaged).
Halfords is quoting for an HCB063 battery, which they sell for £70 in the shop, not £75.
Your car will work fine with that, even if you have S&S... but if you have S&S the battery ought to be an 096AGM. These have higher capacity, so your S&S will like that battery more. The HCB063 is great while it's in new condition but a year or two from now, it'll degrade a bit and lose its Mojo.
On the other hand, if the battery discharges frequently (through lack of use) your battery life will be short anyway, so there's no point in fitting a twice-the-price 096AGM for now, only for it to go flat often and then die the same way. Just keep buying new HCB063s.
Secondly... if the engine turns over and squeals, it could be a starter/flywheel problem but that sound is metallic/fingernails on the chalk-board, not a sound like "squealing tyres", which is the Auxillary (aux' aka "fan" aka alternator) belt.
If your b/f or anyone needs to work out which it is for sure, get them to *carefully* squirt some WD40 onto the inner run of the belt as the engine is running (don't stand in line with the belt or you'll get a face full of WD40). If that keeps it quiet for a few days, then that's the culprit.
If your belt is loose (press down on it while the engine isn't running..

If it has any "give" in it... more than 1cm could be too much... it is more likely to be the belt. If your belt looks old, dry, cracked or very shiny on the inner face, then it's also likely to be the belt.
With any luck, it's the original factory belt and it's just dry and withered a bit. A new battery and (in your own time) a new belt will sort it.
The cam-belt is a different animal .. it lives under the black cover and also drives the water pump. Change it, its tensioner/pulley and the pump when the weather's warmer).
Ralf S.