Bit of a radical thought, but bear with....
Seeing as though 75-80% of asylum claims are upheld, why not open a claims centre in France, say Calais.
Staff the centre so that all applications can be resolved within an agreed timescale, say 28 days.
If successful, arrange transport to the UK.
If unsuccessful, allow 1 appeal after say 6 months. If this appeal is successful, transport is arranged.
If it is unsuccessful tell the applicants why and state that they will not be allowed to enter the UK.
As fingerprints will be taken at the application stage, if anyone then comes over by any non-official means they are returned to France.
This way, the UK don't have to house them whilst applications are being processed.
(I realise this is what used to happen prior to the Conservatives and Brexit, but now we have adults in charge, it must be time to revisit the idea).