It is obvious that you do not know which area is most suitable for you to buy a house within your budget. There would be many factors that may influence people who are planning to buy a new house. If you do not want to undergo the eligibility process for taking a house loan to buy a house, then it is good that you know the from one lender and then continue to search for a house in the loan amount that could be raised by you. Also, there are situations, where your plans would get deviated because of the reason that your earlier lender may not be supporting the new area that you are searching for to find a lovely home.
Though the new area you have started searching for is falling out of the city in which you are working in, you could eventually find a job in the new area where you found your lovely house. So, your decision should not be based on the lender support, it should rather be based on your likes and dislikes. Hence, better choose the best lender and then know the areas covered by them. When you make a list of the Rivingtons areas covered you would be happy to know that it supports wide areas and hence you could be free to search for a house of your choice within your budget.
Also, since the lender would not force you to pay the capital amount and interest both together, you could plan to pay only the interest and then plan to clear the house loan by selling you ancestor properties or by selling your investments in shares when the market is up. Just be cautious enough to do a right selection so that you do not incur any loss.