The mutuals have launched fixed and discount variable products.
Hinckley and Rugby’s products include a five-year fix at 3.59 per cent and a two-year fix at 3.39 per cent.
Both come with a £199 arrangement fee and £800 completion fee.
A two-year discount variable at 3.09 per cent is also in the range and comes with the same fee structure
It is 2.80 per cent off the society’s standard variable rate (SVR) for two years before reverting to 1.65 per cent discount off the SVR for the next three years.
At 85% LTV there is a five-year fix at 3.09 per cent, a two-year fix at 2.79 per cent and a two-year discount also available at 2.39 per cent.
Carolyn Thornley-Yates (pictured), head of mortgage proposition and distribution at Hinckley & Rugby Building Society, said: “We’re keen to offer lending solutions for all borrowers irrespective of the size of their deposit.
“Launching a product which opens up access to Hinckley & Rugby’s individual lending policy at 90 per cent LTV, as well as releasing some competitively priced products for both residential and landlord borrowers at the lower end of the LTV spectrum, widens choices for intermediaries and borrowers alike.”
Meanwhile, Scottish Building Society has reintroduced 90 per cent LTV mortgages for properties in Scotland.
The deals are across its residential range of mortgages, including for new-build and flats.
The two-year fix is at 3.49 per cent, three-year fix at 3.19 per cent and five-year version at 3.68 per cent – all have a £995 fee.
A pair of three-year discount products are also available at 2.99 per cent and 3.29 per cent, with and without the £995 fee respectively.