Not sure what you mean by non-availability of ammunition. Most small fully automatic weapons - MAC-10, Uzi, MP4, MP7A1 - fire 9mm which is the world's most popular handgun cartridge.
So the only situation where there might be a shortage of ammunition is if you didn't bring enough with you.
No genuine firearm dealer in the UK will sell a member of the public ammunition unless they present a valid Firearm Certificate showing permission to possess ammunition of that caliber as the law requires the sale be recorded on the certificate. I don't know any legal gun owner who would sell some of their ammunition to some criminal type "off the books" as they are responsible people and the penalties are just too severe. I know I wouldn't. If someone approached an owner or dealer and tried to buy ammunition off the books then it is highly likely the person approached would call the Police for their own protection.
This pretty much leaves smuggled ammunition and Customs do a good enough job of keeping that out that it isn't freely available on street corners.
9mm is a rare caliber for a private gun owner to have on their certificate as the number of guns in that caliber that can be owned by the public in the UK is quite small. .38 Special and .357 Magnum are the two most common pistol-based calibers for legal weapons in our club.