Whether you are able to prevent this third party from trading in this manner depends on a number of factors, most important of which is whether your trading name or brand is unique to you and has been registered as a trade mark.
If your brand name is registered as a trade mark relating to the goods or services which this third party is selling, it is likely that you can take action in relation to an infringement of your registered trade mark rights. If your brand is not a registered trade mark then the situation becomes somewhat more complex and your chances of success are much reduced.
Related: What is the best way to protect your brand?
If your brand name has been in consistent use since you started trading in 2003 and this use pre-dates the time when the third party began using the brand then you may potentially have the option of using your common law rights in the name as a means of taking action. This is dependent on your brand name not being a generic term (ie a term in general use in your industry) or descriptive and non-distinctive.
In this instance you will be relying on your common law rights in the use of the brand name. Ideally you will have built up these rights through consistent use of the same brand name over the period from 2003 until now as inconsistency can weaken your case. If the third party has been trading using this name since before 2003 then they have probably established common law rights in the name and this leaves you in a very bad position where you may have to adopt a new brand yourselves.
If the brand name in question is a generic term or descriptive and non-distinctive, it will prove difficult to make a case against this third party and having allowed your URL to lapse you have effectively lost control of your brand.
The moral here is that if you have established a brand name you should register it as a trade mark. This will ensure that you have the exclusive right to use the name in relation to your chosen range of goods and/or services and can enforce these rights against competing third parties who might adopt identical or confusingly similar brands or use your brand in a URL.
The other lesson is to manage your URLs with care in order to prevent them being taken by competitors.