James Vince’s side sit top of the embryonic Division 1 table after hammering Somerset by an innings and 113 runs in their curtain-raiser.
They were the only two contracted players the ECB made available in the opening round of games last week.
Somerset were missing Craig Overton and Jack Leach, but they are available for this week’s game with Essex at Taunton.
Burns scored 41 and 22 not out in the high-scoring draw with defending champions Warwickshire, while Pope hit 58. A third England Test player, wicket-keeper Ben Foakes, top scored with 132 not out as Surrey posted 428-8 declared at Edgbaston.
Both Burns and Pope will be looking to impress the England selectors after being left out of the recent tour of the West Indies, where Foakes played all three Tests.
Pope only has one Test century to his name in 23 appearances, but boasts a stunning first class average of 72.85 from 35 games for his county.
Hampshire know exactly what he is capable of, having been on the receiving end of four of his 10 Championship centuries. In six first class games against Hampshire, Pope averages 113.28.
His four centuries include an unbeaten 221 in August 2019 and 131 last April when Hampshire were humiliated by an innings and 239 runs at The Oval. On that latter occasion, Pope and Hashim Amla (215) added 257 for the third wicket as Surrey, replying to Hampshire’s 92 all out, posted a huge 560-7 declared.
West Indian seamer Kemar Roach then bagged a career best 8-40 in the second innings as Hampshire suffered their fifth worst innings defeat in Championship history, and their highest since 1911.
Both Amla and Roach have returned to Surrey again this year and are expected to face Hampshire.
Hampshire have only ever won eight Championship games at The Oval, with just three coming since 1967.
The last arrived in 2008 when Nic Pothas (137 not out) and No 8 Dimi Mascarenhas (99) starred in a first innings total of 480-8 declared in an eventual innings success.
Hampshire’s most amazing win, though, arrived in 1982 and was inspired by a magical spell of fast bowling from the legendary Malcolm Marshall.
Surrey only needed 105 to win, but Marshall ripped out the top five as the hosts spectacularly collapsed to 37-7 and later 68-9.
David Thomas (37) and last man Graham Monkhouse added 33 for the final wicket as tensions mounted. But Marshall (7-37) wrapped up victory – by just three runs - when he had Thomas caught by Nick Pocock.