Mortgage Solutions understands the products are to be removed from next week.
The Bank of England base rate is now at its lowest level on record, after monetary policymakers cut it by 50 basis points to help the economy through the coronavirus outbreak.
Lenders’ tracker mortgage pay rates are set to subsequently fall, with changes typically taking effect from the beginning of next month.
It means many trackers have become considerably cheaper than fixed rate equivalents, hence a scramble among lenders to manage demand.
Nationwide two-year tracker rates today increased by 0.15 per cent to new borrowers.
A spokeswoman for BM Solutions and Scottish Widows, which are both owned by Lloyds Banking Group, said: “We regularly review our mortgage products and policies to ensure they meet the needs of our customers as well as listening to customer and broker feedback.
“This only applies to new lending – existing customers with a tracker rate will see a reduction in line with their mortgage terms and conditions.
“A range of fixed rate products is available to new customers.”