* Parcel volume up 38%, letters drop 33%
* Says restructuring plans underway
* Reiterates outlook for 2020-21 (Rewrites throughout, adds detail, shares)
By Yadarisa Shabong and Pushkala Aripaka
July 21 (Reuters) - Britain's Royal Mail said its parcel shipments rose 38% in April-June as lockdowns drove a surge in online shopping, but letter volumes slid by a third, adding to pressure on its main legacy business.
The former postal monopoly, which has stressed the need to transform into a parcel-led business as letter volumes decline, is embarking on another round of cutbacks after the departure of German boss Rico Back in May following a year of union resistance to restructuring.
Chairman Keith Williams kicked off talks earlier this month with the company's largest union in a bid to push through changes and shore up long-term profitability.
Royal Mail said on Tuesday that the talks, which include the integration of Parcelforce into Royal Mail, were progressing.
Between March 30 and June 28, the company's first quarter, Royal Mail said it shipped 117 million more parcels and delivered 788 million fewer letters, or a 33% fall from a year earlier.
The British operation, which is expected to be loss-making this year, had previously said letter revenues fell 23% in April and May, while parcel revenue grew 28%.
"Customers are wanting more parcels delivered to their homes and are sending fewer letters," Royal Mail said. "Advertising mail in Royal Mail continues to be impacted by GDP and low levels of business activity."
Shares in the company, down nearly 20% this year, were up 1% on Tuesday.
The company said there were no changes to its 2021 outlook from June, when it reported a 31% fall in profits and laid out plans to cut 2,000 jobs, largely in back office and some frontline management roles.
$1 = 0.7885 pounds Reporting by Pushkala Aripaka and Yadarisa Shabong in Bengaluru, Editing by Sherry Jacob-Phillips and Susan Fenton