Demand among tenants has jumped for properties where all the bills are included in the rent, according to Rightmove.
The property website said inquiries for build-to-rent homes with bills included had risen by 36% over the past year.
Millions of people are facing rising domestic gas and electricity bills as the cost of living soars.
The prospect of further rises will have increased demand for all-in rent.
Existing pressure on tenants' finances comes as the average monthly rent being advertised across Britain (excluding London) was a record £1,088 in the first three months of the year. That was an 11% annual increase, Rightmove said.
In London, average asking rents have increased by 14% annually to £2,195 per calendar month.
There are also more than triple the number of tenants inquiring as there are rental properties available, making the market highly competitive, according to the website.
Homes with balconies, communal gardens, properties allowing pets and those offering zero deposits were all popular, it said.
Nearly two-thirds (63%) of landlords told Rightmove they have kept rents the same for their tenants over the past year, with the remaining 37% saying they have increased their rents.
Tim Bannister, Rightmove's director of property data, said: "A shortage of rental homes and strong demand for the properties available has led to a greater number of tenants choosing to renew their leases and stay put, rather than re-enter a competitive rental market.
"People who had been waiting to see what happened last year are now being faced with record rents and so are seeking out properties where they can have more certainty over their outgoings, with all bills included becoming increasingly sought after.
"Landlords may have been tempted to put their rents up given the high demand from new tenants, but many understand the affordability challenges of rising rents and bills, as our study shows that the majority are charging their tenants the same as a year ago."
The Royal Institution of Chartered Surveyors (Rics) said earlier in the week that 63% of property professionals expected rents to rise in the next three months, the highest proportion since its records started in 1999.