US citizen kids entering UK with UK passport parent

I will be traveling with my children to the UK this summer and had a question about which line to get into upon arriving in Heathrow. 

I am a dual US/UK citizen and usually travel on my US passport to the UK when traveling with my family who all hold US passports only. Am I eligible to bring my children (age 13 & 9) into the UK/EU line with me because I am a UK citizen or do I need to go in the line for US citizens with them (and use my US passport)?

Am thinking this is not an uncommon scenario and welcome learning how others manage this situation...thanks!

You should always enter the UK on your uk passport, and you can use the UK/EU line with your children. I'm a US citizen but when I travel I use the UK/EU line when I'm with my uk husband and UK child

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Yup, take them through the EU line with you.

Yes, the last time my UK husband came in with me, we went to the non EU line and the border agent said when I travel with him we can go to whichever line is shortest.

Great, I will plan on using the UK/EU line then!  Thanks for the feedback. 

A followup question- in this scenario is it necessary for me to have a notarized letter from my husband allowing me to take our children out of the country/ into the UK? 

Dual US/UK here - I HAVE had to show a notarized letter from my husband at the airport before, when I travel with our girls and without him. On more than one occasion, having that letter (ours is a general permission to go back and forth, not trip specific) has saved us from being denied boarding. Highly recommend it.