The difference between home insurance and specific pump insurance is the pump specific one will arrange for you to have a replacement the next day, home insurance could take weeks. Also not all home insurances cover medical equipment, you do need to check as adding it as a £3k named item may not result in the cover you expect.
When I contacted my home insurance 5 years ago, they told me they would not cover medical equipment. They then cancelled my home insurance without telling me and I only noticed a month later when the monthly payment had not been taken. I asked why it had been cancelled and they told me they could not accept me insuring home based medical equipment with another insurance company and splitting it across two even though they would not provide any cover. Needless to say I changed the home insurance and took out pump specific.