British nationals currently have to apply for visas for spouses, partners and children living in Gaza through the existing family visa route, which carries substantial fees.
For example, someone living outside the UK who wishes to join their British spouse must typically pay £1,840. There is also a health surcharge, costing at least £1,560 per adult.
Relatives such as siblings, parents of adult children and extended family are not eligible for a visa in most cases.
By contrast, the Ukraine Family Scheme – which ended last month – allowed applications from immediate or extended family members, including parents of an adult child. It was free to apply, and additional fees, such as the health surcharge, were waived.
British-Palestinian families have been campaigning for similar tailor-made schemes since the conflict broke out last year.
A previous letter, sent to Foreign Secretary David Cameron in December, was signed by 80 families with relatives trapped in Gaza.
A Home Office spokesperson said teams in Cairo, and at the Rafah crossing, were providing consular assistance to British nationals trying to leave Gaza.
“We currently have no plans to establish a separate route for Palestinians to come to the UK,” he said, adding that dependants of British citizens who need a visa can apply for one through the established channels.