Normally each side pays their own costs in applications such as these. However, in the circumstances you describe I doubt that it would be reasonable for your wife to be disadvantaged because you have a deeper pocket than she does. What she could do is apply to the court for maintenance pending suit and for that application to contain provision for her.
I would suggest that you look at this link and, in particular, paragraph 38 of the judgement.
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www.familylawweek.co.uk]
In this case the wife had absolutely not funds to pursue a legal claim against her wealthy ex husband. The court dealt with that by ordering him to pay her a lump sum in order to be able to pay her legal costs.