Andy Craig comes in for Kevin Utterson at centre and Nathan Hines replaces lock Stuart Grimes.
In the replacements, Ross Beattie steps in for Jon Petrie who drops into the A squad for the game against England A at Northampton.
While Craig's inclusion was tactical, Hines' place in the side was partly due to his extra freshness.
Newcastle Falcons lock Grimes played in last weekend's victory over Leicester in the Zurich Premiership.
McGeechan said: "Obviously, Scott Murray's line-out work is outstanding and was against Wales.
"Nathan is a ball-carrier, which will be particularly important against England where there will be a lot of rugby played.
"We also know that the two of them have had a full two weeks to recover which is another consideration."
But the Scotland coach believed the combination of Craig and Bordeaux-Begles centre James McLaren at Twickenham would be "interesting".
He added: "We looked at the reasons we gave those tries away in the last few minutes and Andy is a very good and alert defender.
"We have been impressed with what he has been doing and it makes an interesting combination in the centre with James McLaren.
"We are also looking at the next opposition - England. We are looking all the time at our tactics and they have to vary the way we deliver them."
Scotland team to face England:
Backs: G Metcalfe (Glasgow); C Paterson (Edinburgh), J McLaren (Bordeaux-Begles), A Craig (Orrell), K Logan (Wasps); G Townsend (Borders), B Redpath, capt (Sale).
Forwards:T Smith (Northampton), G Bulloch (Glasgow), B Douglas (Borders), S Murray (Edinburgh), N Hines (Edinburgh), J White (Glasgow), S Taylor (Edinburgh), A Mower (Newcastle).
Replacements: R Russell (Saracens), G Kerr (Leeds), S Grimes (Newcastle), R Beattie (Bristol), M Blair (Edinburgh), G Ross (Leeds), K Utterson (Borders).