The only thing your neighbours can do is to ask your local authority to issue a “Community Protection Notice” (CPN). The Anti-social Behaviour, Crime and Policing Act 2014 provides for these. However, the LA is unlikely to accede to their request. As the name suggests, the legislation is designed mainly to address anti-social behaviour and whilst this is a broad term, it would be hard to regard feeding birds in your own garden as “anti-social.” Regarding the issue of notices, the legislation says this:
1)An authorised person may issue a community protection notice to an individual aged 16 or over, or a body, if satisfied on reasonable grounds that—
(a)the conduct of the individual or body is having a detrimental effect, of a persistent or continuing nature, on the quality of life of those in the locality, and
(b)the conduct is unreasonable.
It will be a stretch for your neighbours to show, to the LA’s satisfaction, that your feeding the birds and them consequently messing on their car is “…having a detrimental effect, of a persistent or continuing nature, on the quality of life of those in the locality.” It would also be difficult to show that your conduct is unreasonable. It is not unreasonable to put food out for birds in your garden. More than that, it would be difficult to show that the birds are using the tree as their preferred place to defecate simply because you put food out for them. I think my reaction to such a request would be to say that if you park your car under a tree, you should be prepared for birds' mess to fall on it.
In the unlikely event your LA does grant a CPN you can appeal to the Magistrates’ Court. You can do this on the following grounds:
1.That the conduct specified in the community protection notice—
(a)did not take place,
(b)has not had a detrimental effect on the quality of life of those in the locality,
(c)has not been of a persistent or continuing nature,
(d)is not unreasonable, or
(e)is conduct that the person cannot reasonably be expected to control or affect.
I would think, from what you have described, that any reasonable Bench would find that (b) and (d) apply.