Finding the qibla without a compass
Plenty of phones have no magnetometer at all — most tablets, many budget handsets, and every laptop. Plenty of others have one that cannot be trusted where you happen to be standing. The bearing in degrees still works; it just needs something other than a needle to apply it to.
1. The sun and a shadow
This is the most reliable method available to anyone, because sunlight cannot be deflected by a radiator. As the sun climbs from sunrise towards due south it sweeps through every bearing in between — including, from Britain, the qibla at around 115° to 122°.
At the moment the sun sits on that bearing, stand a straight object upright in the light — a pen, a bottle, the edge of a door frame. Its shadow falls along the qibla line, pointing directly away from Makkah. Face back along the shadow and you are facing the qibla.
The timing is the fiddly part, and it moves through the year. In midsummer the sun rises well to the north-east and crosses the qibla bearing mid-morning. In the depths of winter it rises to the south-east, already past that bearing, and the method does not work at all — for a few weeks around the solstice you have to use one of the others.
2. A map and a known bearing
Take the bearing for your city from the table on the front page and open any map of where you are, with north at the top. Draw or imagine a line from your building at that angle — a little south of east-south-east — and see what it runs along or towards: a road, a railway, a river, a tower block on the horizon.
That landmark is now your qibla. Indoors, the same trick works with the walls: once you know which wall of the room the line crosses, you can face it without any instrument at all, and it will still be there tomorrow.
Use the true-north column for this. Map north is true north; the magnetic column is only for an actual compass needle.
3. The street you are on
British streets in most towns were laid out on a grid or along a valley, and once you have established the qibla against one of them you have it for the whole neighbourhood. It is worth working out once, carefully, at home — and then it is a fact you carry around rather than something to look up.
A note on mosques
If there is a mosque nearby you already have an answer that was worked out with more care than a phone can manage: the mihrab wall. Note which way it faces relative to the street outside and you have a reference for the whole area.
Occasionally an older mosque was aligned by a method that has since been improved on and sits a few degrees off. That is worth knowing and not worth worrying about — the margin the jurists allow is far wider than the disagreement, as the accuracy page sets out.