Whittlesey is linked on several occasions to other Romany Gypsy families in the same sort of era:
Josiah Smith, son of Josiah Smith 'Gypsey' and Mary buried at Whittlesey, Cambridgeshire on 21st April 1797.
Honour Boswell, daughter of Ladger Boswell and Sarah, 'Gypsies' baptised at Whittlesey, Cambridgeshire on 6th March 1802.
Hezekiah Boswell, son of Vato Boswell and Cinderella Boswell (nee Hall) baptised at Whittlesey, Cambridgeshire, March 1825.
The birth of Elijah Herring was registered there in autumn 1837. He was the father of Leopolus 'Poley' Herring/Heron. They were prominent members of the famous fortune telling encampment at Blackpool Pleasure Beach from 1890-1915. The Rev. George Hall writes of them in his 1915 book 'The Gypsies Parson'
As these all occurred either in early spring or autumn, I would think maybe they visited this place for some sort of regular agricultural work, rather than using it as a winter stop over.
The only Samuel Gray I have in my records was the son of Collingwood Gray and Frances Crosby who was baptised in 1812, so doesn't seem to link to your people.
The Bird family are recorded living an itinerant lifestyle as early as 1732, when Elizabeth Bird, a vagrant: 16 years old, was taken ill in Hagley, Worcestershire . She described her father and mother as ‘wandering people’. She had received parish relief in Clent but was moved on as she had ‘stayed long enough’. She then became very ill and crept into a barn from where she was taken to the house of the Overseer at Hagley. In March 1849, the famed Matthias ‘Matty’ Cooper, appeared before the Lent Assizes in Sussex charged with poisoning a pig at Ferring, Sussex alongside members of the Lee and Bird families. Uriah Cooper, a relative of Matty, is recorded in a tent at Holty Common, Hartfield, Sussex on the 1851 census, next to Kezia Cooper, his probable sister, her husband Joseph Junix and several members of the Bird family. In 1861 three ‘Gipsies ‘ Riley, Levina and Alfred Bird are listed as sleeping in a barn at Covington, Northamptonshire next to families of Smiths, Davies and Fletchers in caravans. In 1881 Elijah Bird ‘No occupation; a Gipsy’ is recorded with his family, sleeping in a barn at Wistow Fen, Huntingdon. So your Samuel Gray and Letitia Bird marriage could definitely be Romany people.