Lied to insurer to cover up accident - can I still claim?

I had a minor accident yesterday morning which was completely my fault - I went into the back of a stationary vehicle.

My vehicle is a write off, but the other vehicle had only a few scratches to the back bumper. As I am only covered for third party I agreed with the other driver to settle the matter privately and not go through my insurer, hoping to protect my no claims bonus and keep my future insurance premiums low.

I purchased another car to replace mine and contacted my insurer yesterday afternoon to transfer my insurance to the new car. I gave a false reason for this, saying that my car had an engine problem which would have been very expensive to repair, and since it was an old car it was simply more sensible to buy a new one.

However now the other driver is being difficult and trying to get money out of me without a repair quote, and I would prefer to involve my insurer. Will it cause problems for me that I spoke to them the day of the accident and lied about it? I am worried that this will invalidate my insurance, and alerting them now will be too late for them to pay out and simply cause even more difficulty for me..