There are two possibilities for James' marriage:
1829 James of St Neots and Rebecca Fletcher at Eynesbury
and
1831 James and Mary Gillings at Toseland
There's a burial at Toseland of Mary Wiles aged 30 on 14 Feb 1837, but it needs reference to the PR to see if she was described as wife of James. But I can't find any subsequent sighting of James. However there are other burials 1816-33 in Toseland, so I think it's possible that James was from that parish. Again it needs reference to Toseland parish register to see if he was baptised there. If he was that would leave the field open for the 1829 marriage to be your James.
There was a baptism of Griffin Fletcher Wiles in St Neots on 27 Feb 1830, son of James and Rebecca, butcher. The BLARS lease that you found to which James Wiles was a party had his address as Provost St, City Rd, London. In 1841 Griffin appears at Brunswick Place, Clerkenwell with George Squire 25, Rebecca Squire 29, Griffin Wiles 13 Not b in Middx, Frances Wiles 10 not, John Wiles 8 b in Middx; Edwin Wiles 6 b in Middx; Rebecca Wiles 2 b in Middx. Still living in Clerkenwell in 1851 were
George Squire 35 b St Neots; Rebecca Squire 40 b Toseland; Edwin Wiles 14 b Clerkenwell; George Squire 9 b Clerkenwell.
There is a death in the GRO index of James Wiles in the Dec quarter 1839 at Islington, but it would take the purchase of the death cert to get more detail, including his age and address. Hopefully it would say Provost St. Clerkenwell which is in the London Borough of Islington, which would at least tie him in with the London family. Provost St is only 100 yards from Brunswick Place
Interesting too that Rebecca Wiles appears to have married a Squire from St Neots. But I can't find a marriage.
When Griffin Fletcher Wiles married in St Pancras in 1850 he named his father as James Wiles dead.
Nor can I see that James and Rebecca baptised any of their London children. However Freebmd has a birth of Rebecca Ann Wiles in Islington in the Sept quarter 1839, but it will take another £9-25 to buy the certificate!
It's a scorcher here today. Went out earlier this afternoon to watch the Tour de France passing through Castelnaudary, a few miles from here. Too hot! And it's all over in seconds.
Still trying to tie up some St Neots end, but thought I'd post it before the computer overheats
David