salam brother,
there`s nothing to worry about
as long as you both have letters in your name,can proof that u lived together , it`s absolutely fine , bel 3arbi y3ni kollou tamam w ma fich hata mochkel

all wat u need is to pray to god and it`s guna be fine.
You have savings and your wife is allowed to claim benefit!
in other sense ; let`s say u was not married to ur wife and u still in egypt m, ok . She will still receive all the benefits . you are not affecting the asmount of money she is getting,it`s for her and your child, tax credit , housing benefit and council tax benefit are claimed by your wife , because she have the right to have them as a british citizen. Also you are not claiming jobseeker allowance and income support as these one proof that u cannot support ur family and u need more money from the government.
Your situation is fine and inchallah everything will be fine,it`s normal to worry and stress.
dont worry brother it`s fiiiiine
salam