Are you sure about the 95% LTV? I know most lenders offer 90% - 92% max, this can be even less if you are topping up to refinance short term debt.
Anyway, if the value of your house has risen considerably in the last few months you should probably be able to top up now. You don't say who your mortgage is with but usually you can top up 6 months after drawdown.
The process is similar enough to when you first applied for your mortgage and you probably won't need a solicitor, although this depens on the amount of the top up.