if they tried to claim the domain (via an arbitration panel through the UDRP) by asserting ownership of the trademark, they would lose because the domain name was registered before the trademark was applied for.
Trademarks (in the UK) are both a registered and an unregistered right.
You get a trademark by using a mark that is suitable to identify the source of goods or services. A website, for example, is a service and so their is an automatically established IP right for the original owners.
Marks are registered in a particular ["Nice"] classification and only protect against other following uses in that same classification.
Strictly (at least in Europe, AFAICT) someone else can use your mark in your field of commerce too provided there is no cause for confusion as to the origin - eg disparate geographical locations. But cost of lawyers and the assumption of confusion tend to rule against this.
To get that domain through UDRP they shouldn't stand a chance if registration date of the domain is before trademark or use. It couldn't be registered in bad faith no matter what they were using it for. Of course, there are all sorts of terrible judges on UDRP panels and it's like russian roulette.