As for the question, you can apply for injunctive relief and, if you can show financial loss, sue in a defamation claim.
The injunction a court order requiring the competitor to do something or refrain from pursuing a course of conduct.
However, before you do this, (and as you alluded to already) you should send a cease and desist letter to warn them of your intentions unless they stop (and give them 14 days to stop their conduct to allow them to seek legal advice). A template “cease and desist” letter is available at LawDepot
If you go to the search box in the top right corner of the site, it will bring up a list - you want the "general" letter.
You can use your own letter if you wish - it just has to make it clear this is a cease and desist letter, that you demand they stop their conduct, and that if they do not within 14 days you will apply to the court for the injunction and seek your costs.
That letter may well be enough to stop the conduct - as an injunction is a serious legal remedy. The judge will want to see that you have sent the cease and desist letter given an injunction is a last resort.
Assuming they continue, you will need to complete the application for the injunction and send to your county court.
If the injunction application is successful you can ask the court for a costs order to be paid by the defendant.
If granted, the Order is then served on the individual concerned and they are bound by the court order - if they breach the order, they are in contempt of court and could well face a fine and/or a prison term of up to 2 years.
The order will say they must stop their conduct with immediate effect. They are very effective given the consequences of breaching the terms of the injunction.
The cease and desist letter will hopefully work so you may not need to apply but if you then I recommend you ask a law firm to assist. I have set out a few choices for you - they should be able to claim their costs from the competitor so it would be worth asking them to help you with this:
Brett Wilson LLP: Specialist Regulatory & Litigation Solicitors London
Solicitors in Leeds, LS6 | Whiterose Blackmans | A Trusted Leeds
Routh Clarke Solicitors