a statement sets out (allegedly) exactly what a child's needs are. and then how those needs are best met (in terms of hours of support/SALT/OT etc), as well as naming the school which will meet those needs.
usually, the LA try it on - eg dd1's very first statement proposal was for 7 hours (non-specified) support a week. we rejected it, and after a lot of to-ing and fro-ing, she is at a SN school, with full time 1:1. there is not a second where she does not have 1:1 support, including breaktimes and lunchtimes. this is what she needs.
a statement shoudl set out, in quantified hours, what support is needed, and from what professional.
then, as a statement is legally binding, the LA is duty bound to provide that support. La's try to get away with wooly statements, which do not specify or quantify support - ie "X needs access to a differentiated curriculum, and up to 12 hours a week of support within the classroom', rather than 'X needs 4 hours per week of individual SALT, delivered by a qualified porfessional, and small group teaching, in a group of no more than 3, for 12 hours a week' (or whatever)
if you have a well written statement (everyone on here can help with that, as well as IPSEA etc), then it doesn't matter whether the LA and the school have already spent their SEN budget - not your problem. they are legally obliged to deliver what is set out in the statement. they have to find the money, or the staff, or the provision - whatever it is (as long as it is listed in part 3, not in other sections, otherwise they fob you off and say it is a health issue, or similar, so that it comes form another budget).
this is why LAs hate issuing statemtns, because it means you can hold them to account, and make them provide what your ds needs. as it stands, they could grant you HLN funding, and then pull it after a week - no rigths, no obligations, and your ds is back to being part time, without proper support.