Company A owns the .co.uk version of the domain name; company B bought the .com version, and made it redirect to their own website
Would a legal challenge regarding this have any standing in a UK court, and if so, how would one go about resolving it?
This is called cybersquatting - when you own a trademark and the other registrant has registered the domain in bad faith. There are means for resolving these matters. I have not been able to find any laws specific to the United Kingdom, however there are other laws and agreements this falls under.
However, the respondent (the person owning the domain in dispute) must generally intend to profit from, and have registered the domain in bad faith. They must also have no legitimate interest in the domain name. The applicant must also show that it is similar to their trademark.
You may be able to submit a dispute to ICANN in accordance with their Uniform Domain-Name Dispute-Resolution Policy. The decisions of such arbitration is binding on the parties, and may include cancellation or transfer of the domain, or refusal of the claim.
If you are able to bring a claim in the United States, the Anticybersquatting Consumer Protection Act provides similar protections, and may additionally award damages.
Additionally, the World Intellectual Property Organization provides for arbitration, which allows trademark holders to attempt to claim a squatted site. However, these decisions are not binding on the parties.
What your competitor has done is perfectly legal and a legal challenge would have no chance of success.
If you wanted the .com (or .net or .com.au etc.) complement to your .co.uk you should have bought them. The competition has just as much right to an unowned domain that represents their business as you do.
You could approach your competitor and offer to buy it on whatever terms you can negotiate.
