35% think the rising cost of living is already making it more difficult to give their dogs all they need.
By far the greatest worry was how they would manage to pay vet bills, which 49% named as their main concern.
The second biggest worry was affording dog food (17%), closely followed by insurance (15%).
Non-dog owners in the UK, meanwhile, were asked whether the rising cost of living would prevent them from adopting or buying a dog. Over half (54%) said that it would.
The Dogs Trust says this research mirrors its own experience, seeing a steady increase in the number of requests from owners who have decided to give up their dog.
It harks back to the year after the 2008 recession, when the increase in the number of stray and abandoned dogs reached over 25% in the UK.
Owen Sharp, Dogs Trust CEO, said: "We know from the experience of the 2008 recession that economic crisis can and will lead to people needing to give up their beloved dogs. Sadly, many loving dog owners simply won’t be able to afford to keep them.
“At Dogs Trust we’re rehoming and fostering dogs as quickly as we can - but as soon as we free up a kennel space, there’s a dog to fill it again.
“We’ve already taken 13,000 calls this year from owners who need to give up their dogs – a 58% increase on last year.
“We know that dog owners need immediate help and we’re working hard to find ways to support them - but it takes time.
“However, there are other ways we help, like our Hope Project, which aims to keep anyone experiencing a housing crisis and their dog together, and helping people find other services such as pet food banks or local charities that could ease the burden.”
“We want dog owners to realise that they don’t have to wait until they are in crisis to call us for help.”
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