You can make a current regulator out of a 555.
Use the top one of these circuits I posted above.
COnnect pins 2 and 6 of the 555 where the input of the MCP1401 goes
Connect pin 3 where the output of the MCP1401 goes.
Connect pin 4 and pin 8 to V+, and pin 1 to 0V.
Decouple pin 5.
The 555 will do an adequate job of driving a MOSFET gate, the MCP1401 does it better.

 

Why not just use a 555 PWM?
Its cheap and simple.

Also has lower efficiency.
Since the OP is using battery power for the LED, that is likely not acceptable.

 

Also has lower efficiency.
Since the OP is using battery power for the LED, that is likely not acceptable.

The battery is driving huge current loads as to that compared by the current draw of a 555 driver.
I doubt the 555 driver will be of concern.
The 555 can be changed to CMOS version if needed.

 

he battery is driving huge current loads as to that compared by the current draw of a 555 driver.

I'm not talking about the current draw of a 555 timer (which indeed is small).
I'm referring to the difference in efficiency between a non-inductor PWM circuit (which uses a resistor to limit the current, [R1 in your circuit] and has essentially the same efficiency as any linear regulator), and an inductive switching current-regulator, which has over 80% efficiency.
Measure the efficiency of your 555 circuit in LTspice and you will see what I mean.

 

I'm not talking about the current draw of a 555 timer (which indeed is small).
I'm referring to the difference in efficiency between a non-inductor PWM circuit (which uses a resistor to limit the current, [R1 in your circuit] and has essentially the same efficiency as any linear regulator), and an inductive switching current-regulator, which has over 80% efficiency.
Measure the efficiency of your 555 circuit in LTspice and you will see what I mean.

Tradeoff for parts that are easily available…

 

Tradeoff for parts that are easily available…

Then I guess it's up to the OP to decide if he can tolerate the low efficiency of the 555 PWM circuit (about 20% for 1 LED powered by a 12V battery) .

 

Then I guess it's up to the OP to decide if he can tolerate the low efficiency of the 555 PWM circuit (about 20% for 1 LED powered by a 12V battery) .

If he's got a 555 but not a MOSFET driver, then my circuit in #41(modified to suit a 555) is efficient enough - not quite as good as your circuit in post #14, because it has a higher voltage across the current sense resistor; but he does need an inductor.

 

he does need an inductor.

Yes, the inductor is critical to getting reasonably good efficiency.