Mr Naylor admits he 'has to be careful'about UCLH's past industrial relations problems.
But cleaning, catering and portering staff are being transferred to a private firm in February, after a long battle by the Unison branch, which secured a landmark conditions deal.
Now, branch secretary Candy Udwin says: 'Stewards have met the company and put in a claim for new staff to be paid the same money. '
Staff shortages are still 'a big issue', so the union is calling for the Elizabeth Garrett Anderson site - soon to be sold off by the trust - to be made into affordable social housing for health workers and local people.
And Ms Udwin is 'proud'that the branch 'and all the people who supported us'held off the PFI deal long enough for it to be 'the one without bed cuts'.