INHouse said the move will see Oliver support the agency’s ambitious plans for investment and growth, as well as providing senior counsel to iNHouse clients.
Bunhill and INHouse have partnered in the past. For example, they pitched for and worked together on the successful campaign for the Scotch Whisky Association to freeze excise duty in the last Budget.
INHouse, whose retained clients include Centrica, Diageo, NHBC and The Hyde Group, was founded by Perrior and business partner Jo Tanner in 2006.
Pauley said: "Jo and Katie have built a really great business with a unique capability to deliver results for their clients. I’m very excited to help them realise the next stage of their ambitions for iNHouse."
In a statement, Tanner and Perrior said: "We are enthusiastic for what the future holds at iNHouse and are thrilled that we will be able to draw on Oliver’s experience. There is considerable potential for growth and Oliver is a significant asset who will add real value across the business. We are very much looking forward to working together".
Perrior, who like Tanner has been a long-time Conservative activist, departed iNHouse for Downing Street shortly after Theresa May became Prime Minister in 2016. She resigned after the PM called a snap General Election the following year and later return to iNHouse as chair.
Pauley departed Portland in 2017 after six years to set up his own agency. Before Portland, he was at FleishmanHillard, most recently in the London public affairs team.
In February this year, iNHouse announced the appointment of Theresa May's former director of strategy and chief speechwriter Chris Wilkins, alongside former Jeremy Corbyn advisor Paul Ovenden.
Last year, PRWeek reported that Michelle Di Leo had departed iNHouse, which she joined from FleishmanHillard Fishburn as a partner, after around six months.