Private housing tenants are stepping up their campaign against letting agents' "rip-off" fees which the former housing minister John Healey has branded "unfair and unjustifiable".

Angry tenants are targeting branches of Foxtons and Felicity J Lord estate agents on Saturday following Healey's call in parliament this week for the fees to be banned because they are contributing towards a nationwide "silent crisis in the private rented sector".

Tenants have reported being forced to pay more than £500 in various administration fees to secure a privately let home, on top of a month's rent and deposit. Foxtons charges new tenants £420 as an "administration fee", £210 to change a tenant's name on the contract and £96 to renew terms. Felicity J Lord charges £165 per property "for tenancy agreement" and £65 per person "for reference checks", a £60 "admin fee" and £120 "check-in fee". Tenants also report having to pay a holding deposit of £1,000 which is forfeited if they fail the reference check.

"This is a market without rules and it is too common for letting agents to charge often huge upfront fees for … any range of excuses," said Healey. "It adds several hundred pounds or more to the upfront cost of getting a basic private let. Many people have no option but to find the cash, so they are often going into debt at the very start of their tenancy."

A private member's bill calling for the government to ban the fees had its first reading this week in the Commons, with cross-party backing including Tory former minister Peter Bottomley. The fees have already been banned in Scotland. The housing charity Shelter has calculated the average cost of upfront fees charged by letting agents is almost £350.

"Letting agents need to recognise that renters are tired of being ripped off and treated badly," said Heather Kennedy, organiser of Digs, an east London tenants group. "More and more tenants in Hackney and across London are now getting organised and standing together, demanding fair treatment from letting agents and landlords. The government needs to recognise that in a city where demand for affordable housing far outstrips supply, regulation of letting agents is desperately needed to protect renters from the worst excesses of an overheated rental market."

A spokesman for Felicity J Lord said its fees were "extremely competitive" and "anecdotal feedback we get tends to show that tenants don't mind paying a reasonable fee as long as they receive a commensurate level of service". Foxtons declined to comment. A group of four people who renew a Foxton's tenancy once and change one name on their tenancy agreement could find themselves paying more than £800 in administrative fees.

One of the protesters, Rosie Walker, said that when she moved into a flat in Stamford Hill, the agent – not Foxtons or Felicity J Lord – asked for a £150 security fee and £100 signing fee on top of the deposit.

"When I asked what 'security fee' meant, they explained that it was highly recommended because 'this landlord could get difficult when it comes to returning the deposit'," she said. "In the criminal world, this is called protection money."

Speaking in parliament this week, Healey had said: "The basic regulation now in place for estate agents is still missing for letting and managing agents. The private rented market is now failing too many despairing tenants who feel let down by low standards and ripped off by high fees. This sector has been called the property market's wild west."