More than 115,000 staff walked out on Friday, with more strikes to follow in the run-up to Christmas.
Recent talks between the CWU union and Royal Mail have broken down.
Members of the union are expected to continue striking on Sunday as well as on 14, 15, 23 and 24 December.
Although there are no letter deliveries on Sundays, there are parcel deliveries, and Royal Mail also processes mail on a Sunday for delivery on a Monday.
Last week, Royal Mail advised people to post Christmas mail earlier than usual due to the strikes.
Millions of letters have reportedly been piling up as negotiations have stalled, while it has brought forward the final suggested date for sending second class post to 12 December from 19 December, and for first class to 16 December from 21 December.
The union has said staff want a pay rise that matches the soaring cost of living and has accused management of trying to "force through thousands of compulsory redundancies".
Workers carrying placards demanding the removal of Royal Mail's chief executive Simon Thompson gathered outside the Mount Pleasant Mail Centre in London - the company's largest sorting site in the UK.
One employee Nick, who has worked for Royal Mail for 38 years, told the BBC that although he had walked out during previous strikes, the distance between management and unions appeared to him to be wider in this wave of industrial action.
"It seems to me there's not really a negotiation. It is a take it or leave it deal where they are attacking our terms and conditions."
Inside the sorting office, parcels and letters continued to be sorted by a skeleton crew of 100 people, compared to the 1,000 employees who normally work at the centre.
Dave Ward, the CWU general secretary, said: "Royal Mail bosses are risking a Christmas meltdown because of their stubborn refusal to treat their employees with respect.
"Postal workers want to get on with serving the communities they belong to, delivering Christmas gifts and tackling the backlog from recent weeks.
"But they know their value, and they will not meekly accept the casualisation of their jobs, the destruction of their conditions and the impoverishment of their families."
Talks have broken down between the union and Royal Mail, a spokesman said, adding that Royal Mail managers are "refusing to budge with their 'best and final' offer".
That offer includes a 9% pay deal over 18 months and "a number of other concessions to terms and agreements", Royal Mail said.
A spokesman said: "We spent three more days at [conciliation service] Acas this week to discuss what needs to happen for the strikes to be lifted.
"In the end, all we received was another request for more pay, without the changes needed to fund the pay offer," he said, adding that the union "knows full well" that the business is losing more than £1m a day.