Forecast vs full
The four reasons your forecast is lower
The starting-amount rule
On 6 April 2016 the DWP calculated a starting amount for everyone as the higher of: (a) what they would have got under the old rules (basic + SERPS/S2P) and (b) what they would have got under the new rules (full £155.65 in 2016 minus COPE)1. That starting amount is the base your forecast builds on. Post-2016 qualifying years each add about £6.89/wk until you hit the £241.30 cap.
If COPE is the reason
You can lift the figure by adding qualifying years after 6 April 2016 (paid Class 1 or voluntary Class 3) until your figure hits the £241.30 ceiling. Whether that fully closes the gap depends on how many post-2016 years you have already banked and how many you have left before SPA2.
If gaps are the reason
Buy them. Class 3 voluntary NI costs £923/year for the year and adds £6.89/wk to the forecast. The payback period after SPA is about 2.6 years, so it is one of the highest-return decisions available to most UK pre-retirees3.