Would the UK grant a transit visa to a person it deported five years ago?

The eligibility requirements for a transit visa or leave to enter for transit include the applicant being able to satisfy the decision maker that they: (a) are genuinely in transit to another country outside the common travel area, meaning the main purpose of their visit is to transit the UK and that the applicant is taking a reasonable transit route; and (b) will not access public funds or medical treatment, work or study in the UK; and (c) genuinely intend and are able to leave the UK within 48 hours after their arrival; and (d) are assured entry to their country of destination and any other countries they are transiting on their way there. With a deportation history, transit through the UK may not be deemed a reasonable route unless it is the only one possible from the country of origin, and it will likely be very difficult to convince the decision-maker that intentions to leave are genuine.