Actually, that's not QUITE true. He may have been registering his dissatisfaction with the way the investigation was proceeding. He was within his rights to do so. HOWEVER, it was entirely down to the police if they allowed themselves to be influenced by anything he said. One reads statements such as "He/she made me do it". This is rarely true. We usually have a choice. So whatever it was you imagine he may have been responsible for 'making' the police do, it would have been their choice.
The police did say 'no' to 'the relatives'. The police explained to 'the relatives' how Sheila was the killer and 'the relatives' at least in-part, were able to come to a reluctant acceptance that she could have carried out the killings. However 'the relatives' began an attempt to 'infiltrate' and influence various police ranks - some of whom were familar with the customs and historic relationships in that particular area of Essex. The police again said 'no' - even at one point questioning whether they were prepared for a potentially innocent man to go to jail. One particuilar relative replied in the affirmative. Even when Robert Boutflour's chosen stooge was manovering in to position and asking for a case review, the police still came back and said 'no - the evidence indicates Sheila Caffell'.
'The relatives' had to resort to using a channel between themselves, Ainsley and Stan Jones (more than willing to do to Ainsley and the relatives' bidding), in order engineer a situation were Julie Mugford was facing a precipice and could be manipulated in to constantly changing statements with the aim of achieving a desired result. They also had to collude in order to come up with a bogus physical exhibit! This latter circumstance is even accepted by some who favour guilt!
The real police did say 'no' to the relatives. The problem was that Jeremy lent himself to being framed, by virtue of three factors - his position vis-a-vis 'the relatives' and the relevant estate / financial / land matters, his own behaviour in the aftermath of the killings; and his perceived character among 'the relatives' prior to the killings. The actual evidence regarding the crime had to be invented!