People are looking to pets to provide company, while they are unable to see friends and family due to social distancing measures.
Animal shelters say there has been a noticeable rise in the number of people looking to foster or rehome a pet during the coronavirus outbreak.
Centres run by Battersea Cats and Dogs Home and The Dogs Trust have been closed to the public because of COVID-19, but people are still able to enquire online and visit by appointment.
Battersea Cats and Dog Home say it has experienced an "increased interest in rehoming" because of the disease.
"Over the last week we have rehomed nearly 100 animals, with 26 animals rehomed across our three centres on Thursday alone," the organisation said.
"We are striving to arrange the collection of dogs and cats that are currently on reserve, so there may be some delay in responding to new enquiries.
"But we urge anyone looking to bring a little joy in to their lives during these uncertain times to make an appointment at one of our centres as soon as they are able."
The animal shelter has also received an increase in offers to foster an animal, but said it has suspended new applications in order to prioritise working with existing staff and volunteers.
The Dogs Trust said it has received "an overwhelming number of enquiries... not only to rehome dogs permanently but also to foster our dogs on a temporary basis".
However, it said it was important people thought carefully about the decision before taking home a new pet.
"Dog ownership is a wonderful thing but it is a lifelong commitment which must be carefully considered," the trust said.
"As our saying goes, 'a dog is for life' and, in this case, not just for self-isolation.
"We really need people to think about what might happen the other side of this outbreak when people are hopefully back to their usual routines and have other commitments.
"If someone isn't sure about whether now is the right time to welcome a four-legged friend into their home permanently, we would encourage them to support rescue dogs in other ways, such as sponsoring one of our beautiful dogs."
The RSPCA also said it had received an increase in the number of people looking to foster an animal.
However, it encouraged people who were considering it to also consider donating to the charity, "so we can continue rescuing animals during this difficult time".