Convicted rapist Malcolm Millman, 58, was caught on CCTV at Leeds rail station just before 9am on Sunday October 25.
Thames Valley Police say Millman absconded during a day visit to a monastery in St Margarets, Great Gaddesden, at about 2pm on Saturday October 24.
He failed to return to Chadwick Lodge, a secure facility in Milton Keynes, whose care he was under.
Millman was last seen at Manchester Airport railway station on Monday 26 October at around 12.30pm.
Police would like to speak to anyone who may have seen Millman in Leeds or elsewhere.
Police do not believe Millman has access to a passport and therefore is still in the country.
Millman was convicted of rape in 1996 and poses a risk specifically to women and girls.
He could be violent and he has previously threatened his victims with a weapon.
Police are also appealing for health workers to report any potential sightings of Mr Millman as he will now urgently need medication for existing medical conditions including heart disease and diabetes so it is likely that he will need to visit a GP surgery, chemist or emergency department..
Det Supt Chris Ward, from the Thames Valley Police Major Crime Unit, said: “We need the public to let us know if they see anyone matching Mr Millman’s description, particularly NHS staff or other health workers who may come into contact with Mr Millman as he tries to obtain the medication that he needs.
“Please be vigilant in hospitals, surgeries and pharmacies, and help to spread the wanted appeal with posters and leaflets in your waiting rooms and staff rooms.
“If you see Mr Millman, do not approach him and call 999 immediately. Mr Millman is a dangerous sex offender who has a number of previous convictions including for rape. In some of those cases he used a weapon in his attack.
“Any piece of information, no matter how insignificant it may seem, could be vital to tracing Mr Millman, and ensuring this dangerous sex offender is no longer on the streets posing a threat to the public."
If sighted, members of the public should not approach him but should call 999 immediately.
Anyone with information about Millman’s whereabouts should call Thames Valley Police via 101.