wwelvaert,
Nice to see some useful replies have come in.
Regrettably for flights like yours that may drop out of the lower levels of controlled airspace the UK system is often not very joined up and first time operators find this out the hard way.
If you were taken off your flight planned route by ATC then ATC should have okayed this with you first.
Had you been able to fly your planned route and been inside CAS the whole flight you would have kept the same squawk. It's the dropping out of CAS and then the airways controllers doing their best to get rid of you that leads to the numerous squawks and the requests for what service you want once you've left CAS. As mentioned, not a joined up system.
Once you get down to LAM and the London TMA the airspace can be quite complicated. I'd guess that you were vectored from LAM and passed east abeam London City at 4,000ft. If there are any arrivals/departures from City, they will be at 3,000ft at the point you pass abeam the airport hence you likely at 4,000ft. Once you pass City it then may not leave much time or room to get down from 4,000ft onto the Biggin ILS, especially if there was a tailwind hence possibly why high and not ideally positioned.
There are few private pilots in UK ATC these days and even fewer that have ever flown in the airways system themselves in GA type aircraft. Few even go on available fam flights in the larger stuff. The end result of that is awareness of your workload and problems/issues is regrettably not that great to non-existent. Hopefully this thread and any more like it might make some some sit back and think a little rather than fire off the pointlessly obnoxious stuff seen earlier.
Do keep posting and asking questions as and when you need and hopefully they'll be answered reasonably.