The £5m project was backed by members of the cabinet during a meeting on Tuesday.
Members agreed with recommendations from the council’s environment panel that the installation of shared-use paths – for pedestrians and cyclists – through several villages along the route needed ‘further consideration’.
The meeting was told that, of the 436 people who took part, 257 (59 per cent) supported the scheme and 148 (34 per cent) did not.
During the meeting, concerns were raised by groups such as ChiCycle and the West Sussex Cycle Forum about safety, whether the scheme would reduce speeds along the A259 and whether cyclists would even use the new facilities.
Liberal Democrat group leader Adrian Moss described it as ‘flawed’, saying it needed to be changed.
A report to the meeting said that alternative ideas for the route put forward by the Chichester & District Cycle Forum and a number of parish councils had been deemed ‘not technically feasible’.
Alan Sutton (Con, Fittleworth) accepted that the scheme was ‘far from ideal’ but stressed that the current designs would be ‘far from the final plan’.
Insisting that the cabinet was listening to people’s concerns, he added: ‘There’s been an awful lot of work in the background to take into account the various views and to try to come to a sensible solution that not only represents the residents and the users but gives us the opportunity to do something for the future.’
Mr Sutton said he understood some of the frustration being voiced over the plans, adding: ‘There are very strong feelings around this issue – and feelings are always the things that are most difficult to deal with.
‘What we’re dealing with here is a decision that isn’t based on feelings, it’s based on facts.’
Roy Briscoe (Con, Westbourne) added: ‘This is the start of the process – these are the initial proposals.
‘It can and will develop. I’m absolutely certain about that.
‘We also have to be mindful that, through the villages, some of the areas will be turned into 20mph areas.
‘Hopefully it will have an impact, it will provide additional safety measures for cyclists, pedestrians and car users.’
Mr Briscoe reminded the meeting that, in 2017, a lack of local support led to improvements on the A27 being scrapped by the Secretary of State.
He added: ‘I’d hate to see that be the case for this because it does offer some improvements.’
It was a concern which was also touched on by Edgar Vila Pouca, the National Highways programme manager.
He warned: ‘Currently the funding is allocated. Should we decide to start again we would need to put a new bid in.
‘There are no guarantees at all that you would be successful.’
As for the route itself, Mr Vila Pouca said: ‘Ideally we would like to segregate traffic from cyclists and cyclists from pedestrians and we’ve done that on part of the route where we can.
‘Where we can’t, we’ve followed the guidance.
‘The guidance is very clear and it prefers to put cyclists mixing with pedestrians rather than vehicles where we have vehicles of the significance that we do along this section of road – and at the speeds that they do travel along there.
‘Within the scheme, we’re looking at reducing speeds and we need to work with West Sussex on that.
‘We’re also having conversations about reducing the width of the carriageway.’
Pointing out that 13-15,000 vehicles use the A259 every day, Mr Vila Pouca said only the most confident of cyclists currently risked using the road.
The new scheme would open up the route to all.
He added: ‘We do have ideas for improving the scheme but those ideas need to be discussed with [the county council} in a technical matter if the scheme is to proceed to the next stage of design.’
The cabinet noted those discussions and asked for the district council to be consulted on any changes to the scheme.