From Ipswich I assume that your lift will be going down the A12 towards London. However, if you're starting closer to Bury St Edmunds, the A11/M11 route might be a better option. That obviously makes a difference as to which rail stations are easily accessible!
If you can persuade the person giving you a lift to take the M11 route then stations on Bedford to Brighton line come into play, with Elstree & Borehamwood being one possible option. From there it's a 37or 38 minute journey into Blackfriars, which is a short walk from Embankment.
Using the A12 route, your best option might be Stratford and then the Jubilee Line to Waterloo or Westminster. Although it's an Underground service the trains are modern, airy and rarely crowded (certainly not at the Stratford end of the line, so you'd have no problem getting a seat).
If your driver was going to take you as far as Abbey Wood, he/she might as well go a little bit further. Plumstead is easily accessible but the traffic tends to get rather heavy around Woolwich.