Highest totals (team scores) in England v Pakistan test matches.
Javed Miandad. The highest team total in Pakistan vs England test matches is 708 allout, by Pakistan, made at The Oval back in August 1987..

Traditionally a batting beauty, Kennington Oval hosted this last test match on Pakistan's tour of England and visitors won a good toss which nearly sealed the series for them as they had 1-0 lead coming into this match. Opener Rameez Raja and No.3 Manzoor Akhtar missed out but Mudassar Nazar (73), Javed Miandad (260), Saleem Mallik (102) cashed in. Captain Imran Khan nailed in a century late on day two to push visitors in commanding position before they were allout on day 3, breaking their highest ever total against any country, beating 674 for 4 against India.

At that time, it was 6th biggest total by any team and 2nd largest against England. Ian Botham gave away 216 runs from 52 overs he bold, the maximum by any English bowler at that time. But, it couldn't win the game for Pakistan.

Pakistan have gone past 600 run mark versus England 4 times.

Highest total by England in a test match against Pakistan is 558 for 6 wkts declared at Trent Bridge, which they made in reply to 157 allout by visitors and went on to win the match by innings and 129 runs. Denis Compton scored a double century (278) while opener Reg Simpson made a hundred.

Here's a list of totals in Pak v Eng tests, limited to scores larger than 500.

Highest totals (team scores) in Pakistan v England test matches.
Team Total Overs Inns Venue Date
Pakistan 708/10 220.3 1st The Oval 6 Aug 1987
Pakistan 636/8d 156.2 2nd Lahore 29 Nov 2005
Pakistan 608/7d 195.0 1st Bigmingham 3 Jun 1971
Pakistan 600/7d 165.3 1st The Oval 22 Aug 1974
Pakistan 569/9d 192.0 2nd Hyd (Sind) 16 Mar 1973
England 558/6d 139.0 2nd Nottingham 1 Jul 1954
England 546/8d 189.0 2nd Faisalabad 12 Mar 1984
England 545/10 225.4 2nd The Oval 22 Aug 1974
England 544/5d 146.0 1st Birmingham 31 May 1962
Pakistan 538/10 141.4 2nd Leeds 4 Aug 2006
England 528/9d 158.3 1st Lord's 13 Jul 2006
Pakistan 521/8d 159.1 2nd The Oval 22 Aug 1996
England 521/10 169.5 2nd Birmingham 23 Jul 1987
England 515/10 123.0 1st Leeds 4 Aug 2006
England 507/10 233.5 2nd Karachi 2 Feb 1962
Pakistan 505/9d 126.0 1st Manchester 2 Jul 1992
Pakistan 504/10 129.5 2nd The Oval 17 Aug 2006
England 502/7d 175.1 1st Karachi 6 Mar 1969
England 501/10 156.5 2nd Leeds 8 Aug 1996