The other is Sir Mike Rake, one of the UK's most high profile businessmen, who built his name over three decades of service at KPMG, rising to international chairman. He has since been a chair, adviser or president at organisations including easyJet, Worldpay, the CBI, the RNIB, Teneo and Business for New Europe, among others.
Business for New Europe was run by Lucy Thomas and chaired by Rudd, who went on to work on Britain Stronger In Europe, the official 'Remain' campaign in last year's EU Referendum.
Following the 'Leave' vote, Stronger In became Open Britain, a pressure group to "fight against the hard, destructive and potentially chaotic Brexit path the Government has chosen".
Rudd remained its chair, and the group campaigned for a number of MPs across different parties in last month's General Election. Open Britain's registered office is at the same address as Finsbury's HQ.
Gieve has worked at Finsbury for close to two years, having previously been a civil servant in the Cabinet Office.
His role at Finsbury involves working closely with Rudd's office, co-ordinating between the various divisions of the firm and consulting on policy issues.
Gieve is the son of Sir John Gieve, a former senior civil servant who was deputy governer of the Bank of England from 2006 to 2009.
Open Britain's 10-strong board also includes names from across politics and business such as Lord Mandelson, Trevor Phillips, the TV presenter June Sarpong and Innocent Drinks co-founder Richard Reed. It is supported by around 10 full-time employees.
Rudd's sister is the Home Secretary and MP for Hastings Amber Rudd - who campaigned for 'Remain' in the Brexit vote.