Legal advise IPO brand infringement

We are registering a trade mark with the IPO office. We searched and there were no conflicting trade mark names in that category and the IPO itself did not flag any conflict or potential problems. We have been written to by a big law firm on behalf of a huge company that has a similar name in a similar field (catering foods - our name is for a retail food brand) which we had not even thought of as relevant to us. The letter that was sent to us is high-handed and threatening - it talks of infringement, passing off, etc. It asks us to desist immediately. No objection or opposition has been raised by them at the IPO through the PN7A process which makes me think they are not sure they would win going down that route. But I assume there are many other ways they could make life difficult for us. It would be good to have initial advise from a trade registration mark expert.