You could try to recover the sum via the small claims procedure of the County Court � though it is by no means certain that you would succeed.
The much heralded �high hedge� scheme is a typical example of the way government and local councils spin a good yarn. Everybody thought they would simply contact their local council about their neighbour�s 50 foot hedge and the next morning it would be cut down. The realitry, however, is somewhat different.
The measures were included in the Anti-Social Behaviour Act of 2003. However, this was simply a vehicle of convenience to enable the legislation to be enacted. It is accepted that there is no anti-social behaviour or offence committed (unless the hedge owner refuses to comply with the Council�s decision) and no penalty can be imposed simply for owning a high hedge.
As a result, authorities are not investigating any offence - none has been committed, even if a complainant 'wins' their case - and so the legislation does not deal in innocent or guilty parties. As a result, the fee is a payment for a service - not a penalty.
The Act clearly states that complainants must pay a fee to the Council when they submit their hedge complaint. Councils are free to set this fee at any level they think fit and most, as you say, charge around �300.
There is no procedure under the Act for the complainant to obtain re-payment of the fee, either from the Council or from the hedge owner. Unless reimbursement is forthcoming from the Council as jake suggests, the small claims court is the only remedy. The chances of success will depend very much upon what other efforts (prior to the involvement of the Council) were made to settle the dispute and what efforts since then have been made to recover the fee.