Copies of old letters sent to a young boy in a care home by a Labour peer now at the centre of paedophile allegations reveal how the politician cultivated an extremely close relationship with the teenager over a two-year period.

The letters, which have been seen by the Observer, raise serious questions about the peer's motives. Several are signed with "love from" and show how the peer was assiduous in writing to the boy and arranging for them to meet, sometimes in a hotel. The boy, now a married man with children, has alleged that he was sexually abused by the peer.

The existence of the letters – if not their content – has been known about in many quarters for many years. Despite allegations about the peer, no action was taken and he was robustly defended by a number of politicians, including at least one prominent MP who has been openly critical of the government's response to allegations of historical child abuse by MPs and peers.

Last Monday, home secretary Theresa May announced a wide-ranging inquiry into public bodies' and institutions' handling of historical child abuse allegations, to be headed by retired judge Lady Butler-Sloss. The inquiry would include allegations of historical abuse involving politicians.

David Cameron has said there would be no stone left unturned in the search for the truth. In the case of the now elderly peer at the centre of abuse allegations, however, newspaper reports suggest that he may not be questioned by police because of his failing health.

The Observer has also learned that information held by Conservative whips – including details of any sexual misdemeanours – has been shredded since 1996, meaning the Butler-Sloss inquiry is highly unlikely to be able to access much of the secret information logged about the private lives of Tory MPs.

The letters start in 1975 when the peer, then an MP, met the boy when he came to the House of Commons on a visit. The letters reveal how the MP arranged for the boy to help him in his surgery and to do work experience at the Commons. In one early correspondence, the peer, who the Observer is not naming for legal reasons, thanks the boy "for your thoughtful help to me on Sunday – you are an excellent right-hand man!" and arranges to meet him at a Holiday Inn. He signs off "Why not write to me?" and gives his home address.

The correspondence reveals how the peer actively pursued the young boy. "Your letter was very welcome," the politician writes. "I expect that mine to you came as a surprise! Anyway thanks for writing. I enjoyed hearing from you – and having you with me on Tuesday. Fond good wishes to you."

Another letter declares: "I was very pleased to see you on Saturday and to have the chance to discuss so much with you." It continues: "Write to me when you have time. And don't forget to ask whether you can help me at my surgery" before signing off "With fond greetings." A third letter states: "Your letter arrived this morning – and I was pleased to hear from you. I am very glad that you found our chat useful – so did I – and I shall not forget my promises to you."

Given that the MP was in his 40s and the boy barely a teenager, the tone of the letters is striking.

"I was happy to be with you," the politician declares. "And hope that we are achieving some mutual understanding. Straight talk – and total frankness – is essential to our friendship."

The correspondence, much of it on parliamentary notepaper, reveals that the young boy stayed at the politician's London home at least once.

One letter says: "It seems strange not to have you flipping around like a friendly flea! In fact – I miss you."

The boy said that the politician bought him toys and took him to restaurants. Another alleged victim claims that he was seven when the peer sexually assaulted him.

Butler-Sloss, who has faced calls to stand aside because of her links to the establishment she is investigating, has been asked to look into claims of an establishment cover-up of child abuse. But a number of Westminster's alleged perpetrators – such as the former Liberal MP Cyril Smith – are now dead, raising questions about what any inquiry can achieve.

It is said that police have compiled a dossier detailing complaints against the peer which has been passed to the Crown Prosecution Service. The CPS is expected to make recommendations on how to proceed in the autumn.