The petition calls on candidates to do everything they can to protect the health service should they be elected as MP for the area.
It says that includes opposing privatisation, ensuring there is sufficient funding and keeping the NHS out of TTIP (Transatlantic Trade and Investment Partnership) to "protect it from US health corporations".
Local campaigner Nijam Rahman said he had invited all five candidates in Feltham & Heston to collect a copy of the petition outside Holy Trinity Church, in Hounslow High Street, on Wednesday (April 22).
He said Liberal Democrat candidate Roger Crouch, UKIP's Peter Dul and Labour's Seema Malhotra all attended, but Green Party candidate Tony Firkins had been unable to make it and Conservatives Simon Nayyar had declined the invitation.
The issue is particularly close to Mr Rahman's heart as he gave up his job to help care for his mother Rohmun, who had been in hospital after she had a stroke.
He said she was at West Middlesex Hospital for six months until her death last December, aged 78, and he was disappointed with how she was looked after.
"I thought the level of support was very poor and I want more money to be invested in the NHS so other people don't have to go through what we did," said the 40-year-old, of Hounslow West, who used to work as a brand ambassador for beer manufacturer Kingfisher.
"The NHS is very special and we don't want to lose it; we want to make it better. Hopefully the candidates will listen to our message and realise this is an important issue and they shouldn't play around with the NHS."