getLocalTime = function () {
var utcDateStr = document.getElementById('input').innerHTML ;
var utcDate = new Date(utcDateStr);
var offset = new Date().getTimezoneOffset() * 60000;
var localDate = new Date(utcDate.getTime() - offset);
var localDateStr = localDate.toLocaleString();
document.getElementById('output').innerHTML =localDateStr;
};
<p id="input">0001-01-01T00:00:00</p>
<p id="output"></p>
<button onclick="getLocalTime()">Click</button>
Here's a jsFiddle, although it will only work if you're currently in GMT+1 timezone.
I think it's possibly similar to this other question, but I couldn't find any further info for GMT.