Sir Winston Churchill at his desk at Chartwell
The 75-year-old was mowed down as he left St Thomas's hospital where he was being treated for glaucoma.
He suffered broken ribs and a punctured lung and died after falling into a coma.
Mr Rhodes, of Clapham, south London, never married and had no children but was uncle to a nephew and niece.
The pensioner worked for a window cleaning firm in Croydon before setting up his own business.
London terror attack victim Leslie Rhodes used to clean the windows at Chartwell
He cleaned the windows of Chartwell – Winston Churchill's home – for many years
A client and friend of his Janine Roebuck told MailOnline: “Les was my much loved window cleaner for 20 years.
“You couldn't wish to meet a kinder, gentler man.
“He cleaned the windows of Chartwell – Winston Churchill's home – for many years.
“It was something he was so proud of.
“He told me it was a lovely place to visit and gave me a brochure one time so I took my mum there.
Sir Winston Churchill in his study at Chartwell
“He was retired but would still do a few favours for people I suppose. He was more of a friend.
“It's tragic. I’m very sorrowful not to see him again and that such a sweet soul met such a horrible death.
“He was a very gentle and shy person. He was warm and always smiling and it was a joy to see him on a monthly basis.
“I would always make him a cup of tea and we'd have a chat.
“He was a gentleman in every sense of the word.”
Paramedic teams treat a victim of the London terror attack London mourns terror attack at vigil Fri, March 24, 2017
The world grieves after an attacker killed three people and injured about 40 near parliament in London.
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Floral tributes are left after the vigil in Trafalgar Square, London to remember those who lost their lives in the Westminster terrorist attack
Mr Rhodes was one of four people killed by crazed Kent-born terrorist Khalid Masood who ploughed a hired car into crowds of pedestrians on Westminster Bridge and then ran into the grounds of the Houses of Parliament where he stabbed PC Keith Palmer, 48, to death.
US tourist Kurt Cochran, 54, and London-based Spanish teacher Aysha Frade, 43, also died in Masood’s rampage.