Both reduced products received a Moneyfacts product rating of 'outstanding'.
Both Halifax and Lloyds Bank have made rate reductions.
For purchases, Halifax has cut its 2-year variable tracker rate mortgage by 0.05%, making it the lowest within the sector according to Moneyfacts.
The product is available at 85% loan-to-value (LTV) and comes with a £999 product fee.
Rachel Springall, finance expert atMoneyfacts, said: “House purchase customers searching for a low rate may find this deal attractive and they can also add the product fee to the mortgage advance.
"As a result, the deal earns a Moneyfacts product rating of outstanding.”
Lloyds Bank has also made reduced its 5-year fixed remortgage deal.
Now priced at 1.92% and available at 85% LTV, the mortgage comes with a free valuation, free legal fees and a £999 product fee.
Springall added: “Borrowers looking for a competitive rate and cost-saving incentive package from a well-known high street brand may find this deal enticing. As a result, the deal earns a Moneyfacts product rating of outstanding.”