Thanks guys, I ended up calling the AA, and will take it to a garage to flush out on Monday.
And I haven't been fully truthful with you guys either, due to embarrassment, so I do apologise seeing as how helpful the advice on here has been.
I actually poured the frigging oil in last weekend and have been happily driving around with no snow to worry about anymore! Since the oil warning light came back on I decided to check under the bonnet properly today... and noticed it said "cold" next to the cap and then noticed the engine cap, was ideally placed above the engine saying "Castrol is the recommended oil" (Ironically I bought Castrol oil due to seeing this message in the past, so why I didn't think to actually unscrew that cap, god knows). Been stressing about it all day after I realised what I had done!
So yeah I've got a nice oily mix cooling my car atm, due to driving some 100 miles in total (bursts of 10 miles), but fortunately haven't overheated.
Its a stupid mistake but seems like all it needs is a couple or so cleaning cycles, no permanent damage done. I'm sure it'll be cheaper to DIY, but there's no way this numpty is going to risk that! I don't think I can kick myself hard enough but as said I could've been a whole lot stupider.
Anyway thanks guys.