just out of general interest, if you registered as a limited company within the uk and someone already had the domain but was not registered as a trading company, would they have to cease the domain straight of or would you have to get a solicitor to write them a letter saying they have to or similar? or do something else?

Unfortunatly no. If the domain was purchased before you registered the company/trademark then the owner is free to keep the domain.

Luckily for us, I already had our business up and running for 4 years before deciding to incoporate our's so the domain was already in my possesion.

It's a tough one, but I think the best thing to do is write a letter to the owner, explain the circumstances and offer him a price for the domain(s) in question?

Unfortunatly no. If the domain was purchased before you registered the company/trademark then the owner is free to keep the domain.
Thankfully no rather than unfortunately no.

If someone has the bright idea of registering a name first or has a domain that happens to coincide with a wizzbang idea you have some months or years later then why on earth would you assume you had any right to it?

I am only talking about your business name coming after the domain name - doing it the other way around is wrong.

Having said that, I have quite a few domains and if written to with an explanation and a realistic offer that is in line with the expectations the company has of the website I would relinquished the domain without a second thought but any assumption of "it's my domain" will be quickly rebuffed.

True true..

if you registered as a limited company within the uk and someone already had the domain but was not registered as a trading company, would they have to cease the domain straight of or would you have to get a solicitor to write them a letter saying they have to or similar? or do something else?

Why do you believe that you have any sort of rights to the domain, if the person registered the domain before you registered your business? Try sending a nice letter to the current owner and offer to purchase the domain from them. If they refuse, there's not much you can do about it, solicitor or not.

Since a sole trader is a legal way of trading in the UK, why would a limited company receive special treatment?

If the user is cyber squatting, then you may have a chance at getting the domain without paying extortionate prices.

Since a sole trader is a legal way of trading in the UK, why would a limited company receive special treatment?

A Sole Trader does not receive the same level of brand protection in courts, as there is no " register " of sole traders , You can potentially have 10 sole traders acting under the same name , a sole trader is just a person trading as a trading name , not a legal entity.

Having said that If he registered the domain before you incorporated , Then your only chance is to buy it from him unless you could prove he knew you were about to incorporate under that name and registered it to make a profit by selling it to you.