Lettings agent signed AST on our behalf but removed the break clause and we need to sell?

I would say very few rights if any.

You could try and make a financial offer to the tenant to break the agreement. This can work as people always like free money especially if it is more than the cost of uprooting themselves.

Obviously you could take legal action against the agent but you will have to prove that they were negligent in what they did.

You could try to sell with the tenant still in, and maybe offer an inducement to help with the sale and to move out on completion (or just before).

Advice in the Telegraph in 2013 was as follows:

“Ideally, the best way is to sell with a good tenant still in it. It is worth coming to an agreement that is drawn up by a lettings legal expert. For example, make sure you agree how long the tenant can stay in the property, any required notices are given, they keep the place tidy and clean for viewings and will be happy to move out when required. Personally, I would offer a reduced rent or to pay for the tenants moving costs in return for their help and care.”

Whether the agent has acted questionably very much depends on the terms of business you have with them.
You are now in a fixed term agreement for another year. You cannot escape this.
You could possibly market the property as an ongoing concern with the tenant, if its a viable investment for an investor (i.e 5% or more return). If the tenant co operates reasonably with viewing this will bode well with any new investor and they may be able to stay.

Happy to consider buying it from you – where is it?