pedal straps

[SatNavSaysStraightOn]

Sounds familiar! I've never wanted to go for clip-ins,(having seen a few ridiculous own goals scored), so I still use straps myself. My advice:
(1) Whichever foot you plant on the ground when stopped, make the strap on that side slightly looser than the other one.
(2) Wait until you are going fast enough to freewheel, and traffic conditions are safe enough to look down before putting your 2nd foot in.
(3) Keep practising until you can regularly do it by feel, without the need to look down. Practice makes perfect.
(4) Don't stop on up slopes! Spinning the gears faster on hills makes it hell getting your second foot back in. This has foiled some of my most monumental hill climbing attempts.
Good luck. Expect to be bombarded with advice to switch over to clip-ins.

+1 for ALL of this.
It will become second nature with practice.

Edit: I will add the pedals you have can also make a big difference as well. And on my mountain bike, I have the toe strap through the front of the pedal (there are 2 places it could go through) whereas on my road bike & touring bikes the strap goes through the back of the pedal on the side I stand on.

 

[HLaB]

I found toe straps too inconsistent and changed to clip less (clipped but not strap clipped!).