Are they right? Minor modification or major? This may have come to light if you have had to submit photos of your car to the insurer? The insurance companies also have access to many online car clubs and forums (hence they ask your user name) and monitor them. Or have you had your car in for a claim or had to submit photos? It depends on whether the modification is major or a small item.
Either way you have a choice? If it's small and its an oversight you could try and speak to your insurance company and say that you had no idea your policy would be affected (small stuff - tow bars; heavy duty suspension for pot holes etc; small logo's on bodywork) If it's major (lowering suspension; nitro kits; engine modification etc) you might have to bite the bullet and cancel asap. You want to avoid being deemed a 'high risk?'
If you answer truthfully and it's an oversight (you had no idea this would be classed as a modification) that has only just been done it could be worth contacting your insurance company and explaining that you were going to notify them but have been delayed by unforeseen circumstances etc. However it is unusual for them to tell you that you have a modification? If they accept your premium will go up (because they deem you are a risk) plus an admin fee to alter the schedule. If they cannot insure you because of the modification you have made they will tell you. If the modification came with the car you may have to find another insurer. Someone I know had real problems with this when he wanted a red, white and blue stick on stripes to go on his 'go faster' white hatchback (& he is nearly 70 years old!!) His insurance company would not insure him for the stripes so he had to change company.
Regardless you should be aware that if it is a major accident you are involved in the insurance company will send an engineer to crawl all over your car and look to see if it is road worthy and they will look for any modifications that might give the insurance company grounds to pay out to a third party. (eg replacing barriers - out of hours call out involving road closures, teams of work crews, materials, digger hire etc etc can to run to £100,000 plus) But then the insurance company will come after you and recoup their money (sometimes hundreds of thousands of pounds) from every asset you own (car, house, savings, property, jewellery etc etc) because you have not complied with the terms of the contract of insurance.
So in answer to your question - You might be better cancelling your insurance before the due date.
When you take out insurance it all depends on the wording in the questions that are asked by the insurance company when you submit information for your next quote. If they ask 'Have you ever had insurance cancelled by your insurer' You can answer truthfully - 'No' (that is because you have cancelled it) even though the insurer raised the issue and have not yet cancelled it. If they ask - 'Have you ever been required to cancel an insurance policy' - that is different. It is 'Yes' because the insurance company initiated it. You should answer questions truthfully and carefully.
Be aware that insurance companies share information on a large database. All of the data supplied in multiple online quotes is stored and can be checked.