Dear Mr. / Ms,
I was very concerned when I received your letter of yesterday complaining that the central heating system in your new house had not been completed by the date promised.
On referring to our earlier correspondence, I find that I had mistaken the date for completion. The fault is entirely mine and I deeply regret that it occurred.
I realize the inconvenience our oversight must be causing you and will do everything possible to avoid any further delay. I have already given instructions for the work to have priority and the engineers working on the job to be placed on overtime. These arrangements should see the installation completed by next weekend.