Sir Keir Starmer is alleged to have broken parliamentary rules by failing to declare donations of clothing for his wife Victoria Starmer.
The gifts, from prominent Labour donor Lord Alli, were not initially declared in the register of MPs' interests.
The Sunday Times reported that the Prime Minister approached the parliamentary authorities on Tuesday to make a late declaration after being given updated advice on what needed to be registered.
The Tory part has now demanded a full investigation into the Starmers' links with prominent Labour donor Lord Alli.
A Conservative Party spokesman said: 'It's taken just 10 weeks for Keir Starmer to face an investigation for his conduct.