https://www.gov.uk/arrested-your-rights/legal-advice-at-the-... explains things quite well. IIRC you're obliged to identify yourself when questioned but don't have to give any other details. You then have the right to legal representation, a free independent lawyer is provided on request if you don't have one.

I don't think we have a complete right of silence without - for example - being found in contempt of court.

It won't result in contempt of court, but it will result in a direction to the jury that they're entitled to consider unsupported statements you've made in court (but not earlier) as false.