Fewer than 6,000 boat people are awaiting Hanoi's approval to return after accelerated efforts to clear names following the visit by Foreign Office minister Jeremy Hanley.
More than 1,000 names have been cleared since the visit, some from a list queried by Hanoi.
Teams of Interior Ministry officials have been sent out to help police check information against personal details on boat people sent from Hong Kong.
Vietnam only approves a name once it is sure of nationality, family links and house registration. It wants to ensure every returnee has a house to go to.
'We're keen to solve this issue of clearing names as quickly as possible and co-operation involving all sides is now extremely good,' a Vietnamese official said privately.
British diplomats are demanding quick solutions so the thorny issue of what to do with anyone finally rejected can be tackled well before the handover.