The TV ad, created by CHI, featured various people in need of help because of faulty boilers.
A voiceover states: "Whatever happens, it's warming to know that HomeCare is there for you 365 days a year."
Six people challenged the 365-days claim as they believed the service was not available at weekends or on public holidays.
In response British Gas said the HomeCare service was available 365 days a year but admitted there is a reduced service at weekends and on public holidays.
The company also said it runs a dedicated 24-hour HomeCare helpline but admitted engineers were "not necessarily available" 24-hours a day.
The Advertising Standards Authority upheld the complaint and said the ads could be misleading as British Gas should have stated there are times when it runs a skeleton service.
Additionally a complaint over whether the TV and radio ads misleadingly implied a British Gas engineer would attend a call-out in a short space of time was also upheld.
As a result the TV and radio ads cannot be broadcast again in their current form.
The ASA did turn down a challenge by rival energy provider E.On that the campaign failed to communicate the service's geographical restrictions.
The ASA accepted British Gas' argument that the ads were intended to drive awareness of the HomeCare brand in general.