Probably.
Most major countries honor the trademarks filed in other countries. It's just harder and more costly to enforce if not filed. At least if it's non-generic and you try to use it for the exact same product or service. Even if the TM is not filed in the UK, the company may have a common law trademark that would still cover it based on use.
However, if it's generic, fairly obscure, and you intend to use for a totally different product, you may have a right to use it in that way.