Offer 10% below asking price?

You can make an offer. The Estate Agent is legally required to pass your offer on. Owners can say yes or no.

Your reasons are irrelevant really. Its all about the seller and their position.

The person who bought our last property drove us mad faffing about and asking for daft discounts ("to change decor to buyer's preference") and we were at risk of losing our next property. When, at the last minute, he wanted a reduction, we had to suck it up because we really wanted the next house.

On the other hand, when I was selling my parents' home someone tried to do the same, wanting a reduction at the last minute. It was a probate sale and there was no rush for it to go through so I told the EA to put it straight back in the market and I wouldn't be considering any offers from that couple.

The lack of allocated parking would be a deal breaker for me, but depends on where you are and whether you're bothered. Minor cosmetic issues don't really change the value and are easily changeable over time. If full houses are £250-280k, a flat for £300k sounds expensive? but you know your own area.
Is the area extremely popular, e.g. good transport/schools? Where I live they often go to sealed bids and go for way over asking so 10% less would have no chance, but you can only try and see what happens! Are you in a good position? That makes a massive difference

I wouldn't knock 10% off my house for those reasons, or even contemplate it to be honest. Repainting, minor repairs, fresh flooring are often par for the course when you buy a non new build property to a degree. If it had those things and also a newly fitted bathroom it would be on the market at an even higher price. The parking is what it is, if I were selling and a buyer raised that I'd feel a bit confused, ultimately they knew that was the case ahead of time and are clearly still interested if they are thinking of offering so it can't be a deal breaker for them. 10k off? maybe in the right circumstances - 10% I think is unlikely.

All you can do is submit an offer with your best price and hope for the best, there's nothing reasonable about giving a best offer. I'd expect a no unless there are other circumstances here - eg it's been on the market ages or the sellers need a buyer asap for their own reasons.