The group said the number of addressed letters tumbled 6% in the nine months to December 25, while letter revenues fell 5%.
This comes after a 4% fall in letter numbers in its first half.
Royal Mail said: "We are seeing the impact of overall business uncertainty in the UK on letter volumes, in particular advertising and business letters."
The group signalled an impact from Brexit fears on its letters arm in half-year results in November, when revenues from advertising mail slumped 8%.
It said the trend for marketing mail revenues had remained "broadly similar" in the third quarter.
This offset a stronger performance from its parcels business, which notched up a 3% rise in revenues over the nine months to Christmas Day, with the number of parcels delivered up 2%.
Overall revenues across its UK parcels and letters division fell 2%.
But its European parcels business, General Logistics Systems (GLS), saw a strong festive quarter with revenues jumping 9% over the nine months, helping overall group-wide revenues hold firm on a year earlier.
Moya Greene, chief executive of Royal Mail, said: "Our postmen and women delivered a great service at Christmas, even better than last year, with 138 million parcels handled in December alone.
"Our comprehensive planning, which started much earlier this year, enabled us to deliver this service for our customers right across the UK."
While letter mailings have been in decline for some time, Royal Mail said the third quarter was hit particularly hard as it also came up against an "unusually strong" Christmas a year earlier.
It added: "Letters performance in the prior period benefited from the one-off return of direct delivery volumes and a good performance over the peak period."
Royal Mail's Parcelforce Worldwide business suffered a tough Christmas, with parcel numbers down by 1% amid an "increasingly competitive express parcels market".
But the group saw good growth in Royal Mail account parcels.
It said there was no decision yet over controversial changes to its pension scheme announced earlier this month, which sparked union threats of potential strike action.
The group has launched a consultation with 90,000 staff over plans to switch workers in its costly defined benefit scheme - which links pensions to final salaries - to a defined contribution plan, which carries no guarantees over the ultimate payout.
It said no decisions would be made until after the consultation closes on March 10.
The group added: "Royal Mail has considered members' views, and discussed responses with its unions as part of the pension review process.
"Royal Mail will write to members again once it has made a decision."
Unite union officer Brian Scott said: "The trading update confirms the hard work and commitment of our members to deliver a good service to the public in the run-up to Christmas.
"However, it is extremely disappointing that Royal Mail is boasting about paying employees £500 in dividends when at the same time they are seeking to close their pension scheme, which will cost those same employees thousands of pounds in hard- earned pension benefits."