Claire, 32, of Eye Kettleby, near Melton, is almost six miles into the 26-mile course, which she is walking in a Cyclone robotic suit, called ReWalk.
She was joined for the last mile of yesterday's leg, in south London, by former tennis ace Tim Henman and his wife, Lucy.
"I couldn't believe I was actually there with Tim Henman," said Claire.
"He was my favourite tennis player of them all and it was so strange to see him there in front of me. He's exactly like he is on the telly. I told him he used to put me through hell watching him play."
Claire, who was paralysed from the chest down in a riding accident five years ago, is aiming to complete the route in two weeks to raise thousands of pounds for Spinal Research.
She said: "It was a tiring day and I felt a little sore but having Matt and Tim walk with me really spurred me on – they are both lovely blokes."
Claire is walking in a pioneering suit using motion sensors, electronics and computers to help paraplegics walk again.
Tomorrow's leg will see her pass the Cutty Sark on her way through Greenwich.
More information can be found on her website www.get-claire-walking.co.uk
Below is a short video showing Claire training before the marathon. Other Videos uploaded by Claire can be found here: www.youtube.com/user/clairelom