Free Traffic Legal Advice

I was going down an access road at 10.25 am in order to join a main road in Central London (England). The access road has two lane initially, then an arrow on the road indicating the outside lane should join the nearside lane. I was not speeding.I was in the inside lane (next to the kerb) and a car cut sharply in front of me. It turned out to be an unmarked police car which at this point put the blue lights on, and then cut in front of the car in front of me and then waved me down. I stopped and asked if there was a problem. The female police officer said I should have given way to her. I said I thought I was driving correctly, keeping to my lane. She said I should have given way to her (I scarcely saw her car approach from behind as she was driving fast). I have now received a Conditional offer of Fixed Penalty, which I could accept within the time limit and be fined £100 and have 3 points on my licence or go to court. She quoted Highway Code 143 which I have looked up and there was not a contraflow notice in the location. I believe I was driving correctly . Please advise .

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https://www.ftla.uk/speeding-and-other-criminal-offences/

Is THIS the place where the incident occurred? If so traffic in lane 1 needs to allow traffic from lane 2 to filter in, which may be difficult in heavy traffic. It is obviously difficult to really judge who was at fault here without a video, and bear in mind that the officer may have a video and be able to produce it in court. Realistically the court is likely to prefer the officer's version of events if you take this to court, and that is your only alternative to accepting the fixed penalty. If you take it to court and lose it will cost you much more than £100, there will be an income based fine and prosecution costs of over £600 and possibly more than 3 points. Although it will stick in your throat as you feel you were in the right, I would say that the sensible thing to do here is to accept the fixed penalty.
This has been voted the worst junction in Britain for good reason.