If a full featured HTTP proxy is required, the tinyproxy package is an ideal solution for you as a larger proxy might be unavailable in this environment.

1. install softwares

opkg update
opkg install tinyproxy luci-app-tinyproxy

2. configure tinyproxy

uci set tinyproxy.@tinyproxy[0].enable=1
uci commit
/etc/init.d/tinyproxy enable
/etc/init.d/tinyproxy restart

3. configure transparent proxy redirection

uci set firewall.@redirect[0]._name=transparent-proxy
uci set firewall.@redirect[0].src=lan
uci set firewall.@redirect[0].proto=tcp
uci set firewall.@redirect[0].dest_port=8888
uci set firewall.@redirect[0].src_dport=80
uci set firewall.@redirect[0].src_dip='!192.168.1.1'
uci set firewall.@redirect[0].dest_ip=192.168.1.1
uci commit firewall
/etc/init.d/firewall restart

Note that firewall.@redirect[0].src_dip=!192.168.1.1 option is important, if you missed this option you may not connect to your LuCI. I can't find this option in the LuCI "Network ⇒ Firewall ⇒ Traffic Redirection" page, so be careful if you're using LuCI.