If I Have Equity On My House, Can I Free This Up Without My Repayments Going Up?

If you refinance, you're going to have to pay a mortgage for a longer period of time. If you've paid for five years on a thirty-year mortgage, and refinance to another thirty-year mortgage, you'll have paid for thirty-five years--not good!

If you do a home equity loan (HELOC), you have to pay it back, with interest.

There's no way to "free up" equity in your home unless you sell it and buy a less expensive house, as Boris suggested.

When you refinance the lender would have to give you more money than it would take to pay off your current mortgage - not too likely.  Your best bet would be to trade down.