The tenants of the Oak Tree Lane bungalows have also had to cope with heating their homes with fan heaters.
Shropshire Rural Housing Association and Shropshire Council, which have funded the work between them, say they are disappointed that the situation arose.
They say that the old heating is being replaced with a system that will help tenants keep their bills as low as possible.
Christine L'Ecuyer, one of the residents, said that delays with the work meant they had been living on a building site for weeks.
"We have had not central heating for three weeks and, since the weather got colder, have had to manage with an fan heather. Then we were told we wouldn't have water and had to fill bottles and containers."
"We are all of retirement age and it's been very difficult for everyone."
John Green, chief executive of Shropshire Rural Housing Association, said: “It has been a long-standing plan to improve the energy efficiency of all of our homes, some of which are still using expensive and not particularly effective electric heaters.
“In our six bungalows in Burwarton, we are replacing all the old electric heaters with state-of-the-art central heating which uses air source heat pumps rather than gas.
“With the soaring energy costs, we hope this new system will help our tenants to keep their heating bills as low as possible."
He added: “The contractors carrying out this work have been appointed by Shropshire Council, as the council is match-funding the project, and we are disappointed that some of our tenants were left without hot water and heating over the weekend.
“Once we were made aware of the issue, we immediately spoke to the contractor to urgently address the issue. We visited the bungalows on Monday to inspect the work and reassure our tenants that everything was being done to get the new heat pumps installed as quickly as possible.
“We are grateful to Shropshire Council for part-funding this particular project, which cost in the region of £60,000, and will be discussing our tenants’ concerns with them to ensure that future projects are delivered in a more efficient and effective way.”
Councillor Simon Jones, Shropshire Council's cabinet member with responsibilities for social housing, said: “The council has been liaising with the contractor over the issues and has been advised that it was not possible to complete the planned heating system replacement works last week.
"The contractors ensured all the residents were provided with portable heaters. Although all households had electric showers, unfortunately one of these failed to work.
"It is extremely disappointing that this situation has occurred, however, the contractor has assured us that the residents are all happy now, works have been completed on four bungalows and the remaining works are being completed as a matter of urgency.”