Tracker deals have become increasingly popular in recent weeks
A lender has blamed high demand for the decision to raise the cost of tracker mortgages for new borrowers.
The Woolwich said it was now putting its tracker rate back up slightly after having cut the rate on new deals when the Bank rate was cut last week.
It said the influx of requests after the cut had been "unsustainable".
Lloyds TSB, which also runs Cheltenham and Gloucester, is also increasing interest rates on tracker deals, blaming rate increases by competitors.
Part of the deal when the government agreed to a £17bn investment in the bank to be formed by the merger of Lloyds TSB and HBOS was for it to return lending to homebuyers and small businesses to 2007 levels. However, there has been some dispute over the criteria of this pledge.
Existing tracker rate customers will not see any change in their deals, and would have seen repayments come down when the Bank rate was cut to 4.5% from 5% last week.
Potential new customers with lenders such as Abbey and Nationwide have seen the differential between the Bank rate and the cost of their tracker widen since last week's cut.
They have now been joined by Lloyds TSB, which has raised the cost of its mainstream tracker mortgages by between 0.3 and half of a percentage point.
"We are making these changes to ensure our product range is priced competitively in line with the market," a spokesman said.
The Woolwich, the lending arm of Barclays, did cut the cost of tracker deals last week, but said it subsequently faced high demand because others failed to follow suit. It has now put the cost back up by 0.2 of a percentage point.
"We are seeing unsustainable flows of customers to Woolwich since changes by other lenders left us with some of the only competitively priced mortgages in the market," said Andy Gray, head of mortgages at Woolwich.
"As a result of changes elsewhere in the market we now need to control the flow of business by making some slight increases to the rates on our tracker mortgages."
Mortgage group mform.co.uk said that, in general, lenders were charging a wider differential between the Bank rate and the full cost of a tracker deal than a year ago.
At the start of October, the average lifetime tracker rate was 0.95% above the Bank rate, compared with it being 0.3% above the Bank rate a year before.
Lenders have blamed the stubbornly high cost of lending between themselves for the trend.
The cost of repayments on tracker mortgages automatically drops when the Bank rate falls. Predictions of cuts in the coming months increased the popularity of tracker mortgages in August, according to figures released earlier this week by the Council of Mortgage Lenders (CML).
There was a slight shift in the proportion of borrowers choosing tracker rates, which rose slightly, while the level of those opting for fixed-rate deals in August fell slightly compared with the previous month, it said.
Fixed-rate deals accounted for 58% of home loans granted in August, compared with 31% for tracker deals.
Standard variable rate (SVR) deals accounted for only 3% of deals granted in August, but this figure is predicted to rise in the coming months.
A number of banks have passed on the whole of the Bank rate cut to SVR customers in recent days. Others, as well as the Nationwide, have only passed on some of the reduction.
Only four building societies - Nationwide, Britannia, Melton Mowbray and Beverley - have passed on the cut to SVR customers.
"Mutual organisations are supposed to put their members first, but they clearly haven't in the past week," said Louise Cuming, head of mortgages at Moneysupermarket.com.
"People on SVRs are traditionally those who have struggled to get a mortgage, so they are in even greater need of some relief."
But Neil Johnson, of the Building Societies Association, said that the traditional format of using deposits to lend out again was getting more expensive.
He said any interest rate cuts tended to come some weeks, rather than immediately, after a Bank rate announcement, with building societies taking a longer term view of mortgage lending.
"They are not always playing the short-term game that some of their competitors are," he said.