Only you can decide what an acceptable abbreviation or substitute for your domain might be, but whatever you might choose, you can park the other domain on top of tiptopbirthdayparties.co.uk and anyone using that domainname will arrive at the main
website hosting.
It doesn't seem you're looking very hard — if you want something short to the point of initials I see that 'ttbp' is available in only .net, .eu, .biz, .org.uk, .me.uk varieties but 'ttparties' and 'tiptopparties' are both available in all varieties of TLD — why are you limiting yourself to birthday parties only I am left wondering?