Raggy, how big is your back garden? Have you considered building a patio?
Even the best fake grass, such as Astroturf, suffers from exposure to the UV in sunlight, and all of it is expensive. A patio of manageable size -- think big enough for a barbecue and a picnic table -- would probably cost less, and would be an attractive addition to the property.
Two summers ago, we replaced our enormous back deck with a modest patio made of compressed concrete pavers. Everyone who sees it goes Oooh and Aaaah, it's far less of a maintenance challenge; and I can trust it not to catch fire from the barbecue.