These actions carry a significant level of risk. If the district council decides to proceed with its plans and the parish council resolves to fight them, the final bill may well reach six figures. Does that fall within the normal spending parameters of your council? One could argue that there's no point in starting a battle you are unable to finish.
Legally speaking, setting aside the General Power of Competence, a parish council has no specific power to incur this expenditure from public funds (i.e. precept etc). It can raise funds through a public appeal for this purpose, as long as the purpose is clear and contributors do so willingly. Section 137 does not cover consultancy, Section 222 specifies legal proceedings and public inquiries, and Section 111 is questionable, as expenditure must relate to the discharge of the council's functions and the council has no specific function in this regard.
The broad context of GPoC may permit this type of expenditure, as there is no specific pre-commencement limitation.
You have mentioned the limited role of the parish council as a single statutory consultee and that should be an important factor in any decision to throw money at this problem. I assume you're now beyond the point where you can sit down with the district council to voice your concerns and influence their plans. However unpalatable it may seem, you might just have to take this one on the chin and start planning for a different landscape.