In the interests of re-use being better than just throwing away I'd replace the relevant parts.
Both wheels - You should be able to get replacement 700c wheels for around £100 if you're not too fussed about being light or fast.
Both tyres - Not much, maybe £30
Cables - I can't believe you're including these! A few quid to replace.
Chainset - is it the whole set or just the big ring? Assuming the BB is sound, a new chainset could be yours for between £50-£100. Chainrings for about £25ish.
Pedals - not much, depending on what you want.
Seat - again, not much
Mudguards - about £30
Most of the stuff you've listed is just consumable stuff that will inevitably need replacing at some point. Maybe it's all failed at the same time, which looks bad, but really it's just the kind of stuff that you replace as you go along, it's not a good enough reason for dumping a perfectly sound bike. And all of it is easily to fit and fix yourself. The only thing you might need an LBS to do for you is to tweak the gears after you've replaced the cables.